Mark against the correct answer in the following:
Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{1}{(1+\tan x)} d x=?$ A. 0 B. $\frac{\pi}{2}$ C. $\frac{\pi}{4}$ D. $\pi$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\sqrt[3]{\tan x}}{(\sqrt[3]{\tan x}+\sqrt[3]{\cot x})} d x=?$ A. 0 B. $\frac{\pi}{2}$ C. $\frac{\pi}{4}$ D. $\pi$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} d x=?$ A. 0 B. $\frac{\pi}{2}$ C. $\frac{\pi}{4}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\sin ^{n} x}{\left(\sin ^{n} x+\cos ^{n} x\right)} d x=?$ A. $\frac{\pi}{2}$ B. $\frac{\pi}{4}$ C. 1 D. 0 Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\cos ^{1 / 4} x}{\left(\sin ^{1 / 4} x+\cos ^{1 / 4} x\right)} d x=?$ A. 0 B. 1 C. $\frac{\pi}{4}$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\sin ^{4} x}{\left(\sin ^{4} x+\cos ^{4} x\right)} d x=?$ A. $\frac{\pi}{4}$ B. $\frac{\pi}{2}$ C. 1 D. 0 Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\sqrt{\cos x}}{(\sqrt{\cos x}+\sqrt{\sin x})} d x=?$ A. $\frac{\pi}{2}$ B. $\frac{\pi}{4}$ C. $\pi$ D. 0 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\sin x}{(\sin x+\cos x)} d x=?$ A. $\pi$ B. $\frac{\pi}{2}$ C. 0 D. $\frac{\pi}{4}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{2 \pi}|\sin x| d x=?$ A. 2 B. 4 C. 1 D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi}|\cos x| d x=?$ A. 2 B. $\frac{3}{2}$ C. 1 D. 0 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{-a}^{a} x|x| d x=?$ A. 0 B. $2 \mathrm{a}$ C. $\frac{2 a^{3}}{3}$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{-2}^{1} \frac{|\mathrm{x}|}{\mathrm{x}} \mathrm{dx}=?$ A. 3 B. $2.5$ C. $1.5$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{-2}^{1}|2 x+1| d x=?$ A. $\frac{5}{2}$ B. $\frac{7}{2}$ C. $\frac{9}{2}$ D. 0 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{1}|2 x-1| d x=?$ A. 2 B. $\frac{1}{2}$ C. 1 D. 0 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{-2}^{2}|x| d x=?$ A. 4 B. $3.5$ C. 2 D. 0 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\sqrt{2}} \sqrt{2-x^{2}} d x=?$ A. $\pi$ B. $2 \pi$ C. $\frac{\pi}{2}$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{-a}^{a} \sqrt{\frac{a-x}{a+x}} d x=?$ A. aп B. $\frac{a \pi}{2}$ C. $2 \mathrm{a \pi}$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{1} \frac{(1-x)}{(1+x)} d x=?$ A. $(\log 2+1)$ B. $(\log 2-1)$ C. $(2 \log 2-1)$ D. $(2 \log 2+1)$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{1} \sqrt{\frac{1-x}{1+x}} d x=?$ A. $\frac{\pi}{2}$ B. $\left(\frac{\pi}{2}-1\right)$ C. $\left(\frac{\pi}{2}+1\right)$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{1} \frac{d x}{\left(1+x+x^{2}\right)}=?$ A. $\frac{\pi}{\sqrt{3}}$ B. $\frac{\pi}{3}$ C. $\frac{\pi}{3 \sqrt{3}}$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} x \cos x d x=?$ A. $\frac{\pi}{2}$ B. $\left(\frac{\pi}{2}-1\right)$ C. $\left(\frac{\pi}{2}+1\right)$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{9} \frac{d x}{(1+\sqrt{x})}=?$ A. $(3-2 \log 2)$ B. $(3+2 \log 2)$ C. $(6-2 \log 4)$ D. $(6+2 \log 4)$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{1} \frac{d x}{\left(e^{x}+e^{-x}\right)}=?$ A. $\left(1-\frac{\pi}{4}\right)$ B. $\tan ^{-1} \mathrm{e}$ C. $\tan ^{-1} \mathrm{e}+\frac{\pi}{4}$ D. $\tan ^{-1} \mathrm{e}-\frac{\pi}{4}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi}(\sin 2 x \cos 3 x) d x=?$ A. $\frac{4}{5}$ B. $-\frac{4}{5}$ C. $\frac{5}{12}$ D. $-\frac{12}{5}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 2} \sin x \sin 2 x d x=?$ A. $\frac{2}{3}$ B. $\frac{3}{4}$ C. $\frac{5}{6}$ D. $\frac{3}{5}$ Solution:...
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