Download App

Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_{-a}^a \sin x f(\cos x) d x=$
  • A
    a
  • ✓
    $0$
  • C
    1
  • D
    -1
✓

Answer

Correct option: B.
$0$
(B)
Let $f (x)=\sin x f (\cos x)$
$\begin{array}{ll}\therefore & f (-x)=-\sin x f (\cos x)=- f (x) \\ \therefore & f (x) \text { is an odd function. } \\ \therefore & \int_{- a }^{ a } f (x) d x=0\end{array}$

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 "MCQ" from Definite Integration→Definite Integration — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If in a triangle $A B C,(s-a)(s-b)=s(s-c)$, then angle $C$ is equal to
→
$\triangle ABC$ is formed by $A (1,8,4), B (0,-11,4)$ and $C(2,-3,1)$. If $D$ is the foot of the perpendicular from A to BC , then the coordinates of $D$ are
→
The value of $\cos ^{-1}(\cos 12)-\sin ^{-1}(\sin 14)$ is
→
If a plane has x-intercept l, y-intercept m and z-intercept n, and perpendicular distance of plane from origin is k, then
→

If $f(x)=\left\{\begin{array}{ccc}3\left(1-2 x^2\right) & ; & 0<x<1 \\ 0 & ; & \text { otherwise }\end{array}\right.$
is a probability density function of $X$, then $P\left(\frac{1}{4}<x<\frac{1}{3}\right)$ is

→
If matrix $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 3\end{array}\right]$ such that $A X=I$, then $X=$
→
India play two matches each with West indies and Australia. In any match the probability of india getting $0,1$ and $2$ points are $0.45, 0.05$ and $0.50$ respectively. Assuming that the outcomes are indepecdent, the probability of india getting at least 7 points is.
→
If ABCDEF is a regular hexagon and $\overline{ AB }=\overline{ a }$, $\overline{ BC }=\overline{ b }$, then $\overline{ CD }$ is equal to
→
If $\bar{a}, \bar{b}, \bar{c}$ are three vectors, then $[\bar{a} \quad \bar{b} \quad \bar{c}]$ is not equal to
→
Lines $\frac{x}{1}=\frac{y-2}{2}=\frac{z+3}{3}$ and $\frac{x-2}{2}=\frac{y-6}{3}=\frac{z-3}{4}$ are
→