The value of ^ _ - ^3x ^2x dx is : - Vidyadip

MCQ

The value of $\int\limits^\pi_{-\pi}\sin^3\text{x}\cos^2\text{x}\text{ dx}$ is :

A
$\frac{\pi^4}{2}$
B
$\frac{\pi^4}{4}$
✓
$0$
D
none of these

✓

Answer

Correct option: C.

$0$

$\int\limits^\pi_{-\pi}\sin^3\text{x}\cos^2\text{x}\text{ dx}$
$=\int\limits^\pi_{-\pi}\sin\text{x}(1-\cos^2\text{x})\cos^2\text{x}\text{ dx}$
Let $\cos\text{x}=\text{t},$ then $-\sin\text{x}\text{ dx}=\text{dt}$
When, $\text{x}=-\pi,\text{t}-1,\text{x}=\pi,\text{t}=-1$
Therefore the integral becomes
$\int\limits^{-1}_{-1}(1-\text{t}^2)\text{t}^2\text{ dt}$
$=0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The difference of the order and the degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^3+x^4=0$ is:

The value of $\int_{\pi /4}^{3\pi /4} {\frac{\phi }{{1 + \sin \phi }}\,d\phi ,} $ is

The slope of the tangent to the curve $x = t^2 + 3 t - 8, y = 2t^2 - 2t - 5$ at point $(2, -1)$ is :

If $\mathrm{p}(\mathrm{x})$ be a polynomial of degree three that has a local maximum value $8$ at $x=1$ and a local minimum value $4$ at $x=2 ;$ then $p(0)$ is equal to

The derivative of $\sqrt {\sqrt x + 1} $ is

The angle between a line with direction ratios $2 : 2 : 1$ and a line joining $(3, 1, 4)$ to $(7, 2, 12)$ is

The value of the definite integral $\int\limits_{19}^{37} {\left( {{{\{ x\} }^2} + 3(\sin 2\pi x)} \right)\,dx} $ where $\{ x \}$ denotes the fractional part function.

If $y = 2 sin x + sin 2 x$ for $0 \le x \le 2 \pi ,$ then the area enclosed by the curve and the $x-$ axis is

If $\int {\frac{{{a^x}{e^{2x}}}}{{{b^x}{c^x}}}dx = \frac{1}{k}\left( {\frac{{{a^x}{e^{2x}}}}{{{b^x}{c^x}}}} \right)} + l$ then $k =$

The projection of the join of the two points (1, 4, 5), (6, 7, 2) on the line whose d.ss are (4, 5, 6) is: