Find the area of the region bounded by the parabola
Question: Find the area of the region bounded by the parabola $y^{2}=4 x$, the $x$-axis, and the lines $x=1$ and $x=4$. Solution:...
Read More →Find the area of the region bounded by the curve
Question: Find the area of the region bounded by the curve $y=x^{2}$, the $x$-axis, and the lines $x=1$ and $x=3$. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{1} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x=?$ A. $\frac{1}{2}(\pi-\log 2)$ B. $\left(\frac{\pi}{2}-\log 2\right)$ C. $(\pi-2 \log 2)$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{1 / \sqrt{2}} \frac{\sin ^{-1} x}{\left(1-x^{2}\right)^{3 / 2}} d x=?$ A. $\frac{1}{2}(\pi-\log 2)$ B. $\left(\frac{\pi}{2}-2 \log 2\right)$ C. $\left(\frac{\pi}{4}-\frac{1}{2} \log 2\right)$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{\pi}^{2 \pi}|\sin x| d x=?$ A. 0 B. 1 C. 2 D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{1}^{2}\left|x^{2}-3 x+2\right| d x=?$ A. $\frac{-1}{6}$ B. $\frac{1}{6}$ C. $\frac{1}{3}$ D. $\frac{2}{3}$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: Let $[x]$ denote the greatest integer less than or equal to $x$. Then, $\int_{-1}^{1}[x] d x=?$ A. $-1$ B. 0 C. $\frac{1}{2}$ D. 2 Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: Let $[x]$ denote the greatest integer less than or equal to $x$. Then,$\int_{0}^{1.5}[x] d x=?$ A. $\frac{1}{2}$ B. $\frac{3}{2}$ C. 2 D. 3 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{-a}^{a} f(x) d x=?$ A. $2 \int_{0}^{a}\{f(x)+f(-x)\} d x$ B. $2 \int_{0}^{a}\{f(x)-f(-x)\} d x$ C. $\int_{0}^{\mathrm{a}}\{\mathrm{f}(\mathrm{x})+\mathrm{f}(-\mathrm{x})\} \mathrm{dx}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 4} \log (1+\tan x) d x=?$ A. $\frac{\pi}{4}$ B. $\frac{\pi}{4} \log 2$ C. $\frac{\pi}{8} \log 2$ D. 0 Solution:...
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Question: Mark $(\sqrt{)}$ ) against the correct answer in the following: $\int_{0}^{q} \frac{\sqrt{x}}{(\sqrt{x}+\sqrt{a-x})} d x=?$ A. $\frac{\mathrm{a}}{2}$ B. $2 a$ C. $\frac{2 a}{3}$ D. $\frac{\sqrt{a}}{2}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{-\pi / 2}^{\pi / 2} \cos x d x=?$ A. 0 B. 2 C. -1 D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{-1}^{1} \log \left(x+\sqrt{x^{2}+1}\right) d x=?$ A. $\log \frac{1}{2}$ B. $\log 2$ C. $\frac{1}{2} \log 2$ D. 0 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{-\pi}^{\pi} \tan x d x=?$ A. 2 B. $\frac{1}{2}$ C. $-2$ D. 0 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{-\pi}^{\pi}\left(\sin ^{61} x+x^{123}\right) d x=?$ A. $2 \pi$ B. 0 C. $\frac{\pi}{2}$ D. $125 \pi$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{-a}^{a} \log \left(\frac{a-x}{a+x}\right) d x=?$ A. $2 a$ B. $a$ C. 0 D. 1 Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{-1}^{-2} x^{3}\left(1-x^{2}\right) d x=?$ A. $-\frac{40}{3}$ B. $\frac{40}{3}$ C. $\frac{5}{6}$ D. 0 Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{-\pi}^{\pi} \sin ^{5} x d x=?$ A. $\frac{3 \pi}{4}$ B. $2 \pi$ C. $\frac{5 \pi}{16}$ D. 0 Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{-\pi}^{\pi} x^{3} \cos ^{3} x d x=?$ A. $\pi$ B. $\frac{\pi}{4}$ C. $2 \pi$ D. 0 Solution: If $\mathrm{f}$ is an odd function,...
Read More →Mark against the correct answer in the following:
Question: Mark $(\sqrt{)})$ against the correct answer in the following: $\int_{-\pi}^{\pi} x^{4} \sin x d x=?$ A. $2 \pi$ B. $\pi$ C. 0 D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\tan x}{(1+\tan x)} d x=?$ A. 0 B. 1 C. $\frac{\pi}{4}$ D. $\pi$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\sqrt{\cot x}}{(1+\sqrt{\cot x})} d x=?$ A. $\frac{\pi}{4}$ B. $\frac{\pi}{2}$ C. 0 D. 1 Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{\sec ^{5} x}{\left(\sec ^{5} x+\operatorname{cosec}^{5} x\right)} d x=?$ A. $\frac{\pi}{2}$ B. 0 C. $\frac{\pi}{4}$ D. $\pi$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{1}{\left(1+\tan ^{3} x\right)} d x=?$ A. $\frac{\pi}{4}$ B. 0 C. $\frac{\pi}{2}$ D. none of these Solution:...
Read More →Mark against the correct answer in the following:
Question: Mark $(\sqrt{)}$ against the correct answer in the following: $\int_{0}^{\pi / 2} \frac{1}{(1+\sqrt{\cot x})} d x=?$ A. 0 B. $\frac{\pi}{4}$ C. $\frac{\pi}{2}$ D. $\pi$ Solution:...
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