Download App

Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Evaluate: $\int_{-\pi}^\pi x^{10} \sin ^7 x d x$
✓

Answer

(d) : Let $I=\int_{-\pi}^\pi x^{10} \sin ^7 x d x$
Let $f(x)=x^{10} \sin ^7 x$
and $f(-x)=(-x)^{10}[\sin (-x)]^7=-x^{10} \sin ^7 x=-f(x)$
$\therefore f(x)$ is an odd function.
$\therefore \quad I=\int_{-\pi}^\pi x^{10} \sin ^7 x d x=0$

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $P(A)=\frac{3}{5}, P(B)=\frac{1}{5}$ and $A$, $B$ are independent events then $P(A \cap B)$ is -
→
If $\text{f(x)}=\begin{cases}\frac{1-\cos\text{x}}{\text{x}\sin\text{x}}, & \text{x}\neq 0\\\frac{1}{2} & \text{x}= 0\end{cases}$ then at x = 0, f(x) is:
  1. Continuous and differentiable.
  2. Differentiable but not continuous.
  3. Continuous but not differentiable.
  4. Neither continuous not differentiale.
→
If $\text{I}=\begin{bmatrix}1&0\\0&1\end{bmatrix},\text{J}=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ and $\text{B}=\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix},$ then B equals:
  1. $\text{I}\cos\theta+\text{J}\sin\theta$
  2. $\text{I}\sin\theta+\text{J}\cos\theta$
  3. $\text{I}\cos\theta-\text{J}\sin\theta$
  4. $-\text{I}\cos\theta+\text{J}\sin\theta$
→
The image of the point (1, 3, 4) in the plane 2x - y + z + 3 = 0 is:
→
If $A$ is a square matrix such that $A^2=A$, then $(I-A)^3+A$ is equal to
→
The projections of a line segment on x, y and z axes are 12, 4 and 3 respectively. The length and direction cosines of the line segment are:
→
One hundred idential coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is:
→
Find the value of $\int \frac{\sin ^2 x-\cos ^2 x}{\sin ^2 x \cos ^2 x} d x$.
→
A bag contains 5 red and 3 blue balls are drawn at random without replacement, then the probability of getting exactly one red ball is.
→
Two events A and B will be independent, if
→