Download App

Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^{\pi / 6}\left(2+3 x^2\right) \cos 3 x d x=$
  • A
    $\frac{1}{36}(\pi+16)$
  • B
    $\frac{1}{36}(\pi-16)$
  • C
    $\frac{1}{36}\left(\pi^2-16\right)$
  • ✓
    $\frac{1}{36}\left(\pi^2+16\right)$
✓

Answer

Correct option: D.
$\frac{1}{36}\left(\pi^2+16\right)$
(D)
$\int_0^{\frac{\pi}{6}}\left(2+3 x^2\right) \cos 3 x d x$
$=\left[\left(2+3 x^2\right) \cdot \frac{\sin 3 x}{3}\right]_0^{\frac{\pi}{6}}-\int_0^{\frac{\pi}{6}} 6 x \cdot \frac{\sin 3 x}{3} d x$
$=\frac{2}{3}+\frac{\pi^2}{36}+\left[\frac{2 x \cos 3 x}{3}\right]_0^{\frac{\pi}{6}}-\frac{2}{3} \int_0^{\frac{\pi}{6}} \cos 3 x d x$
$\begin{array}{l}=\frac{2}{3}+\frac{\pi^2}{36}+0-\frac{2}{9}[\sin 3 x]_0^{\pi / 6} \\ =\frac{2}{3}+\frac{\pi^2}{36}-\frac{2}{9} \\ =\frac{1}{36}\left(\pi^2+16\right)\end{array}$

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

The area bounded by $y = 2 - x^2$ and $x + y = 0$ is:
→
If $0 \leq x<2 \pi$, then the number of real values of $x$, which satisfy the equation
$\cos x+\cos 2 x+\cos 3 x+\cos 4 x=0$, is
→
The integrating factor of linear differential equation $x \frac{d y}{d x}+2 y=x^2 \log x$ is $......$
→
The point at the curve $y = 12x - x^2$ where the slope of the tangent is zero will be:
→
If the corner points of the feasible solution are $(0,0),(3,0),(2,1)$ and $\left(0, \frac{7}{3}\right)$, the maximum

value of z = 4x + 5y is _______.

→
$\int \frac{\sin 4 x}{\sin x} d x=$ (Where $C$ is a constant of integration.)
→
The area bounded by the curve $y^2=x^2$, and the line $x=8$ is____
→
The equation of the plane through $(-1,1,2)$, whose normal makes equal acute angles with co-ordinate axes is
→
If $A=\left[\begin{array}{ccc}1 & 1 & 1 \\ 2 & 1 & -3 \\ -1 & 2 & 3\end{array}\right]$, then $M_{23}=$
→
If line $\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$ is parallel to the plane $ax + b y+ cz + d =0$, then
→