Mark against the correct answer in the following:
Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 6} \cos x \cos 2 x d x=?$ A. $\frac{1}{4}$ B. $\frac{5}{12}$ C. $\frac{1}{3}$ D. $\frac{7}{12}$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \sin ^{2} x d x=?$ A. $\frac{\pi}{3}$ B. $\frac{\pi}{4}$ C. $\frac{\pi}{2}$ D. $\frac{2 \pi}{3}$ 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. $\frac{1}{2} \log 2$ B. $(2 \log 2+1)$ C. $(2 \log 2-1)$ D. $\left(\frac{1}{2} \log 2-1\right)$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 2} \sqrt{1+\cos 2 x} d x=?$ A. $\sqrt{2}$ B. $\frac{3}{2}$ C. $\sqrt{3}$ D. 2 Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 4} \sqrt{1+\sin 2 x} d x=?$ A. 0 B. 1 C. 2 D. $\sqrt{2}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 2} e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) d x=?$ A. 0 B. $\frac{\pi}{4}$ C. $\mathrm{e}^{\pi / 2}$ D. $\left(\mathrm{e}^{\pi / 2}-1\right)$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{1} \frac{x e^{x}}{(1+x)^{2}} d x=?$ A. $\left(\frac{\mathrm{e}}{2}-1\right)$ B. $(e-1)$ C. $e(e-1)$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2}(\sqrt{\sin x} \cos x)^{3} d x=?$ A. $\frac{2}{9}$ B. $\frac{2}{15}$ C. $\frac{8}{45}$ D. $\frac{5}{2}$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi} \frac{d x}{(1+\sin x)}=?$ A. $\frac{1}{2}$ B. 1 C. 2 D. 0 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{1 / \pi}^{2 / \pi} \frac{\sin (1 / x)}{x^{2}} d x=?$ A. 1 B. $\frac{1}{2}$ C. $\frac{3}{2}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\cos x}{\left(1+\sin ^{2} x\right)} d x=?$ A. $\frac{\pi}{2}$ B. $\frac{\pi}{4}$ C. $\pi$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 4} \frac{e^{\tan x}}{\cos ^{2} x} d x=?$ A. $(e-1)$ B. $(\mathrm{e}+1)$ C. $\left(\frac{1}{e}+1\right)$ D. $\left(\frac{1}{e}-1\right)$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \cos ^{3} x d x=?$ A. 1 B. $\frac{3}{4}$ C. $\frac{2}{3}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)})$ against the correct answer in the following: $\int_{\pi / 3}^{\pi / 2} \operatorname{cosec} x d x=?$ A. $\frac{1}{2} \log 2$ B. $\frac{1}{2} \log 3$ C. - $\log 2$ D. none of these Solution:...
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Question: Mark $(\sqrt{)})$ against the correct answer in the following: $\int_{0}^{\pi / 2} \cos ^{2} x d x=?$ A. $\frac{\pi}{2}$ B. $\pi$ C. $\frac{\pi}{4}$ D. 1 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 4} \tan ^{2} x d x=?$ A. $\left(1-\frac{\pi}{4}\right)$ B. $\left(1+\frac{\pi}{4}\right)$ C. $\left(1-\frac{\pi}{2}\right)$ D. $\left(1+\frac{\pi}{2}\right)$ Solution:...
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Question: Mark $(\sqrt{)}$ ) against the correct answer in the following: $\int_{\pi / 4}^{\pi / 2} \cot x d x=?$ A. $\log 2$ B. $2 \log 2$ C. $\frac{1}{2} \log 2$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{1}^{e} \frac{(\log x)^{2}}{x} d x=?$ A. $\frac{1}{3}$ B. $\frac{1}{3} \mathrm{e}^{3}$ C. $\frac{1}{3}\left(\mathrm{e}^{3}-1\right)$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{1} \frac{x^{3}}{\left(1+x^{8}\right)} d x=?$ A. $\frac{\pi}{2}$ B. $\frac{\pi}{4}$ C. $\frac{\pi}{8}$ D. $\frac{\pi}{16}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{\sqrt{3}}^{\sqrt{8}} x \sqrt{1+x^{2}} d x=?$ A. $\frac{19}{3}$ B. $\frac{19}{6}$ C. $\frac{38}{3}$ D. $\frac{9}{4}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{2} \frac{d x}{\sqrt{4-x^{2}}}=?$ A. 1 B. $\sin ^{-1} \frac{1}{2}$ C. $\frac{\pi}{4}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{1} \frac{1}{\left(1+x^{2}\right)} d x=?$ A. $\frac{\pi}{2}$ B. $\frac{\pi}{3}$ C. $\frac{\pi}{4}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{1} \frac{\mathrm{dx}}{\sqrt{5 \mathrm{x}+3}}=?$ A. $\frac{2}{5}(\sqrt{8}-\sqrt{3})$ B. $\frac{2}{5}(\sqrt{8}+\sqrt{3})$ C. $\frac{2}{5} \sqrt{8}$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{2} \sqrt{6 x+4} d x=?$ A. $\frac{64}{9}$ B. 7 C. $\frac{56}{9}$ D. $\frac{60}{9}$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{1}^{4} \mathrm{x} \sqrt{\mathrm{x}} \mathrm{dx}=?$ A. $12.8$ B. $12.4$ C. 7 D. none of these Solution:...
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