_0^ /6 (2 + 3 x^2 ) 3x ,dx = - Vidyadip

MCQ

$\int_0^{\pi /6} {(2 + 3{x^2})\cos 3x\,dx = } $

A
$\frac{1}{{36}}(\pi + 16)$
B
$\frac{1}{{36}}(\pi - 16)$
C
$\frac{1}{{36}}({\pi ^2} - 16)$
✓
$\frac{1}{{36}}({\pi ^2} + 16)$

✓

Answer

Correct option: D.

$\frac{1}{{36}}({\pi ^2} + 16)$

d
(d) Let $I = \int_0^{\pi /6} {\left( {2 + 3{x^2}} \right)\cos 3x\,dx} $

$ = \left[ {\frac{{\sin 3x}}{3}(2 + 3{x^2})} \right]_0^{\pi /6} - \int_0^{\pi /6} {\frac{{\sin 3x}}{3}} .6x.dx$

$ = \frac{1}{{36}}({\pi ^2} + 16)$.

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 STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $g:(0, \infty) \rightarrow R$ be a differentiable function such that $\int\left(\frac{x(\cos x-\sin x)}{e^{x}+1}+\frac{g(x)\left(e^{x}+1-x e^{x}\right)}{\left(e^{x}+1\right)^{2}}\right) d x=\frac{x g(x)}{e^{x}+1}+c$ for all $x >0$, where $c$ is an arbitrary constant. Then.

Let $y = y\left( x \right)$ be the solutions of the differential equation, $\left( {{x^2} + 1} \right)^2\,\frac{{dy}}{{dx}} + 2x\left( {{x^2} + 1} \right)\,y = 1$ such that $y\left( 0 \right) = 0$. If $\sqrt a y\left( 1 \right) = \frac{\pi }{{32}}$, then the value of $‘a’$ is

Which of the following function is surjective but not injective

What are the order and degree respectively of the differential equation whose solution is $y=c x+c^2-3 c^{3 / 2}+2$ where $c$ is a parameter?

On $Z$ an operation $^*$ is defined by $a ^* b = a^2 + b^2$ for all $a, b \in Z$. The operation $^*$ on $Z$ is:

A water tank has the shape of an inverted right circular cone, whose semi vertical angle is ${\tan ^{ - 1}}\,\left( {\frac{1}{2}} \right)$. Water is poured in at a constant rate of $5$ cubic meter per minute. Then the rate (in $m/min$) at which the level of water is rising at the instant when the depth of water in the tank is $10\, m$ is

If $p$ and $ q$ are positive real numbers such that ${p^2} + {q^2} = 1$ then , the maximum value of $(p+q)$ is

Choose the correct answer in Exercise:
$\int\frac{\cos2\text{x}}{(\sin\text{x}+\cos\text{x)}^{2}}$ is equal to

${d \over {dx}}[(1 + {x^2}){\tan ^{ - 1}}x] = $

By graphical method, the solution of linear programming problem Maximize $Z = 3x_1 + 5x_2$ Subject to $3x_1 + 2x_2 \leq 18 , x_1 \leq 4 , x_2 \leq 6 x , 1 \geq 0, x2 \geq 0,$ is: