(\integral \_ { 0 } ^ { \pi / 6 } \left( 2 + 3 x ^ { 2 } \ri... | MATH - FUNDAMENTAL DEFINITE INTEGRATION, DEFINITE INTEGRATION BY SUBSTITUTION | SolveeIt | Solveeit

Today, August 18

Question

$\int _ { 0 } ^ { \pi / 6 } \left( 2 + 3 x ^ { 2 } \right) \cos 3 x d x =$

A

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

B

$\frac { 1 } { 36 } ( \pi - 16 )$

C

$\frac { 1 } { 36 } \left( \pi ^ { 2 } - 16 \right)$

D

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

Answer

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

Explanation

Solution

Let $I = \int _ { 0 } ^ { \pi / 6 } \left( 2 + 3 x ^ { 2 } \right) \cos 3 x d x$

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