Question

${\int }_0^{10}se{c}^2(3x+6)dx$

• A. $\frac{1}{3}tan\left({36}^o\right)$
• B. $\frac{1}{3}tan\left(6^o\right)$
• C. $\frac{1}{3}tan\left({30}^o\right)$
• D. None of these

Answer 1

The correct option is D

None of these

$I={\int }_0^{10}se{c}^2(3x+6)dx$

Let $3x+6=u$

$\Rightarrow 3dx=du\Rightarrow dx=\frac{du}{3}$

$I=\int se{c}^{2}u\frac{du}{3}$

=$\frac{1}{3}tan\left(u\right)+c$
$I=\frac{1}{3}tan(3x+6{)}_0^{10}$
$\frac{1}{3}[tan36-tan6]$