Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\sin 2 x}{(a+b \cos 2 x)^{2}} d x$ Solution: Assume $a+b \cos 2 x=t$ $d(a+b \cos 2 x)=d t$ $-2 b \sin 2 x d x=d t$ $\sin 2 x d x=\frac{-d t}{2 b}$ $\Rightarrow \frac{-1}{2 b} \int \frac{d t}{t^{2}}$ $\Rightarrow \frac{-1}{2 b} \int \frac{1}{t^{2}} d t$ $\Rightarrow \frac{-1}{2 b} \int t^{-2} \cdot d t$ $\Rightarrow \frac{t^{-1}}{2 b}+c$ But $t=a+b \cos 2 x$ $\Rightarrow \frac{1}{2 b(a+b \cos 2 x)}+C$...
Read More →Differentiate the following with respect to x:
Question: Differentiate the following with respect to x: $(3-4 x)^{5}$ Solution: To Find: Differentiation NOTE : When 2 functions are in the product then we used product rule i.e $\frac{\mathrm{d}(\mathrm{u} \cdot \mathrm{v})}{\mathrm{dx}}=\mathrm{v} \frac{\mathrm{du}}{\mathrm{dx}}+\mathrm{u} \frac{\mathrm{dv}}{\mathrm{dx}}$ Formula used: $\frac{d}{d x}\left(y^{n}\right)=n y^{n-1} \times \frac{d y}{d x}$ Let us take $y=(3-4 x)^{5}$ So, by using the above formula, we have $\frac{d}{d x}(3-4 x)^{5...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\cos x-\sin x}{1+\sin 2 x} d x$ Solution: We know $\cos ^{2} x+\sin ^{2} x=1,2 \sin x \cos x=\sin 2 x$ $\therefore$ Denominator can be written as $\cos ^{2} x+\sin ^{2} x+2 \sin x \cos x=(\sin x+\cos x)^{2}$ $\therefore$ Now the given equation becomes $\Rightarrow \int \frac{\cos x-\sin x}{(\sin x+\cos x)^{2}} d x$ Assume $\cos x+\sin x=t$ $\therefore \mathrm{d}(\cos x+\sin x)=\mathrm{dt}$ $=\cos x-\sin x$ $\therefore d t=\cos x-\sin x$ $\R...
Read More →Explain the role of neural system
Question: Explain the role of neural system in regulation of respiration. Solution: There are various centres in the neural system that plays significant a role in the regulation and control of respiration. Those are: Pneumotaxic centre, Respiratory Rhythm centre or Medullary inspiratory centre, Apneustic centre and chemosensitive centre. 1. Pneumotaxic centre: It is present in the dorsal part (back) of the pons varoli of the brain. It decreases the time duration of the inspiration and alter the...
Read More →Differentiate between
Question: Differentiate between a. Inspiratory and expiratory reserve volume b. Vital capacity and total lung capacity c. Emphysema and occupational respiratory disorder Solution: a. Inspiratory reserve volume is the maximum volume of air that can be inhaled after normal inspiration whereas expiratory volume is the maximum volume of air that can be exhaled after normal exhalation. b. Vital capacity is the maximum volume of air that can be exhaled after normal inspiration whereas total lung capac...
Read More →For completion of respiration process,
Question: For completion of respiration process, write the given steps in sequential manner a. Diffusion of gases (O2and CO2) across alveolar membrane. b. Transport of gases by blood. c. Utilisation of O2by the cells for catabolic reactions and resultant release of CO2. d. Pulmonary ventilation by which atmospheric air is drawn in and CO2rich alveolar air is released out. e. Diffusion of O2and CO2between blood and tissues. Solution: The correct sequence would be: 1. Pulmonary ventilation by whic...
Read More →Compared to O2, diffusion rate of CO2 through
Question: Compared to O2, diffusion rate of CO2through the diffusion membrane per unit difference in partial pressure is much higher. Explain. Solution: As the solubility of carbon dioxide is much higher than oxygen its diffusion rate through the diffusion membrane per unit difference in partial pressure is much higher....
Read More →Differentiate the following with respect to x:
Question: Differentiate the following with respect to x: $(5+7 x)^{6}$ Solution: To Find: Differentiation NOTE : When 2 functions are in the product then we used product rule i.e $\frac{d(u \cdot v)}{d x}=v \frac{d u}{d x}+u \frac{d v}{d x}$ Formula used: $\frac{d}{d x}\left(y^{n}\right)=n y^{n-1} \times \frac{d y}{d x}$ Let us take $y=(5+7 x)^{6}$ So, by using the above formula, we have $\frac{d}{d x}(5+7 x)^{6}=6(5+7 x)^{5} \times \frac{d}{d x}(5+7 x)=6(5+7 x)^{5} \times 7=42(5+7 x)^{5}$ Diffe...
Read More →State the different modes of CO2 transport in blood.
Question: State the different modes of CO2transport in blood. Solution: 1. In Red blood cells carbon dioxide combines with water and forms carbonic acid. It is an unstable form and gets disassociated into hydrogen and bicarbonate ion. 2. Carbon dioxide is also transported through plasma in the form of bicarbonate ions....
Read More →Name the important parts involved
Question: Name the important parts involved in creating a pressure gradient between lungs and the atmosphere during normal respiration. Solution: 1. Diaphragm 2. Internal Intercostal Muscles of the ribs 3. External Intercostal Muscles of the ribs...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1+\cos x}{(x+\sin x)^{3}} d x$ Solution: Assume $x+\sin x=t$ $d(x+\sin x)=d t$ $(1+\cos x) d x=d t$ Substituting $\mathrm{t}$ and $\mathrm{dt}$ in given equation $\Rightarrow \int \frac{\mathrm{dt}}{\mathrm{t}^{2}}$ $\Rightarrow \int \mathrm{t}^{-3} \mathrm{dt}$ $\Rightarrow \frac{t^{-2}}{-2}+c$ $\Rightarrow \frac{-1}{2 t^{2}}+c$ But $t=x+\sin x$ $\Rightarrow \frac{-1}{2(x+\sin x)^{2}}+c$...
Read More →Name the organs of respiration in the following
Question: Name the organs of respiration in the following organisms: a. Flatworm _________________________________________ b. Birds _____________________________________________ c. Frog- ______________________________________________ d. Cockroach ________________________________________ Solution: a. Surface of the body b. Lungs c. Lungs and moist skin d. Tracheal tubes....
Read More →Complete the missing terms
Question: Complete the missing terms a. Inspiratory Capacity (IC) = _____ +IRV b. ___________________ = TV + ERV c. Functional Residual Capacity (FRC) = ERV + ____ Solution: a. Inspiratory Capacity (IC) = TV + IRV b. EC = TV + ERV c. Functional Residual Capacity (FRC) = ERV + RV...
Read More →Arrange the following terms based on
Question: Arrange the following terms based on their volumes in an ascending order a. Tidal Volume (TV) b. Residual Volume (RV) c. Inspiratory Reserve Volume (IRV) d. Expiratory Capacity (EC) Solution: Tidal Volume (TV) Residual Volume (RV) Expiratory Capacity (EC) Inspiratory Reserve Volume (IRV)....
Read More →A major percentage (97%) of O2 is transported
Question: A major percentage (97%) of O2is transported by RBCs in the blood. How does the remaining percentage (3%) of O2transported? Solution: A major percentage (97%) of O2is transported by RBCs in the blood and the remaining percentage (3%) of O2transported through plasma....
Read More →What is the amount of O2 supplied to tissues through every 100 ml.
Question: What is the amount of O2supplied to tissues through every 100 ml. of oxygenated blood under normal physiological conditions? Solution: The amount of O2supplied to tissues through every 100 ml. of oxygenated blood under normal physiological conditions is around 5ml....
Read More →Cigarette smoking causes emphysema.
Question: Cigarette smoking causes emphysema. Give reason. Solution: Excessive cigarette smoking leads to Emphysema due to the presence of various harmful chemicals like nicotine, tar, sulphur etc. Alveoli walls get damaged due to this....
Read More →Name the primary site of exchange of gases in our body?
Question: Name the primary site of exchange of gases in our body? Solution: The primary site of exchange of gases in our body is Alveoli....
Read More →A fluid filled double membranous layer
Question: A fluid filled double membranous layer surrounds the lungs. Name it and mention its important function. Solution: A fluid filled double membranous layer surrounds the lungs is called Pleura. A fluid filled double membranous layer surrounds the lungs is called Pleura....
Read More →Define the following terms?
Question: Define the following terms? a. Tidal volume b. Residual volume c. Asthma Solution: a. Tidal Volume: Volume of air inhaled and exhaled during a normal breathing cycle without any forced breathing is tidal volume. b. Residual Volume: Volume of air left in the lungs even after forced exhalation is called as residual volume. c. Asthma: It is an inflammatory disease of the airways of the lungs...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{\cos ^{2} x} \sin 2 x d x$ Solution: Assume $\cos ^{2} x=t$ $d\left(\cos ^{2} x\right)=d t$ $-2 \sin x \cos x d x=d t$ $-\sin 2 x \cdot d x=d t$ Substituting $\mathrm{t}$ and $\mathrm{dt}$ $\Rightarrow \int e^{t} \cdot d t$ $\Rightarrow e^{t}+c$ But $t=\cos ^{2} x$ $\Rightarrow e^{\cos 2 x}+c$...
Read More →Match the following and mark the correct options
Question: Match the following and mark the correct options Options: a. A-ii, B-i, C-iv, D-iii b. A-i, B-iv, C-ii, D-iii c. A-i, B-iii, C-ii, D-iv d. A-i, B-ii, C-i.v, D-iii Solution: Option (b)A-i, B-iv, C-ii, D-iii is the answer....
Read More →The oxygen – haemoglobin dissociation curve
Question: The oxygen haemoglobin dissociation curve will show a right shift incase of a. High pCO2 b. High pO2 c. Low pCO2 d. Less H+concentration Solution: Option (a)High pCO2 is the answer...
Read More →From the following relationships between respiratory
Question: From the following relationships between respiratory volume and capacities and mark the correct answer i. Inspiratory capacity (IC) = Tidal Volume + Residual Volume ii. Vital Capacity (VC) = Tidal Volume (TV) + Inspiratory Reserve Volume (IRV) + Expiratory Reserve Volume (ERV). iii. Residual Volume (RV) = Vital Capacity (VC) Inspiratory Reserve Volume (IRV) iv. Tidal Volume (TV) = Inspiratory Capacity (IC) Inspiratory ReserveVolume (IRV) a. (i) Incorrect, (ii) Incorrect, (iii) Incorrec...
Read More →In breathing movements,
Question: In breathing movements, air volume can be estimated by a. Stethoscope b. Hygrometer c. Sphigmomanometer d. Spirometer Solution: Option (d)Spirometer is the answer....
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