Recent questions tagged integration

0 votes
0 answers
1
Determine the volume of the solid obtained by rotating the portion of the region bounded by $y=\sqrt[3]{x}$ and $y=\frac{x}{4}$ that lies in the first quadrant about the ...
0 votes
0 answers
2
Depramine the area of region bounded by $y=2x^{2}+10$ and $y=4x+16$
0 votes
0 answers
3
Differentiate each of the following. $g(x)=\int ^{x}_{-4}e^{2t}cos^{2}(1-5t)dt$
0 votes
1 answer
4
1.Evaluate the following definite integral $\int^{130}_{130}\frac{x^{3}-x\sin(x)+\cos(x)}{x^{^{2}}+1}dx$
2 votes
1 answer
5
0 votes
0 answers
7
$\int_{0}^{1}\tan^{-1} (1-\frac{1}{x})$ d(x) find
0 votes
1 answer
8
What is the difference between Integration and Summation?Which one produces a greater value in the same range?
1 votes
2 answers
10
2 votes
1 answer
11
The integral $$\int _0^{\frac{\pi}{2}} \frac{\sin^{50} x}{\sin^{50}x +\cos^{50}x} dx$$ equals$\frac{3 \pi}{4}$$\frac{\pi}{3}$$\frac{\pi}{4}$none of these
3 votes
1 answer
12
For real $\alpha$, the value of $\int_{\alpha}^{\alpha+1} [x]dx$, where $[x]$ denotes the largest integer less than or equal to $x$, is$\alpha$$[\alpha]$$1$$\dfrac{[\alph...
1 votes
1 answer
13
The value of the definite integral $\int_0^{\pi} \mid \frac{1}{2} + \cos x \mid dx$ is$\frac{\pi}{6} + \sqrt{3}$$\frac{\pi}{6} - \sqrt{3}$$0$$\frac{1}{2}$
0 votes
1 answer
14
The value of the integral $\displaystyle{}\int_{-1}^1 \dfrac{x^2}{1+x^2} \sin x \sin 3x \sin 5x dx$ is $0$$\frac{1}{2}$$ – \frac{1}{2}$$1$
1 votes
1 answer
15
Let $R$ be the triangle in the $xy$ – plane bounded by the $x$-axis, the line $y=x$, and the line $x=1$. The value of the double integral $$ \int \int_R \frac{\sin x}{x...
1 votes
1 answer
16
Let $I=\int (\sin x – \cos x)(\sin x + \cos x)^3 dx$ and $K$ be a constant of integration. Then the value of $I$ is$(\sin x + \cos x)^4+K$$(\sin x + \cos x)^2+K$$- \fra...
1 votes
1 answer
17
The area bounded by $y=x^2-4$, $y=0$ and $x=4$ is$\frac{64}{3}$$6$$\frac{16}{3}$$\frac{32}{3}$
1 votes
1 answer
18
Let $I=\int(\sin\:x-\cos\:x)(\sin\:x+\cos\:x)^{3}dx$ and $K$ be a constant of integration. Then the value of $I$ is$(\sin\:x+\cos\:x)^{4}+K$$(\sin\:x+\cos\:x)^{2}+K$$-\fr...
2 votes
1 answer
19
Let $f$ be a continuous function with $f(1) = 1$. Define $$F(t)=\int_{t}^{t^2}f(x)dx$$.The value of $F’(1)$ is$-2$$-1$$1$$2$