Question

Evaluate the integral
${\int }_0^{\pi /4}se{c}^{2}xdx=$

• A. $e-1$
• B. $1$
• C. $e$
• D. $2$

Answer 1

Answer: (B)

$1$

${\int }_0^{\frac{\pi }{4}}{\sec }^{2}xdx$

$\int {\sec }^{2}xdx=tanx+c$

${\int }_0^{\frac{\pi }{4}}{\sec }^{2}xdx=\left(tanx\right){|}_0^{\pi /4}$

$=\left(\right(\tan \frac{\pi }{4})-(\tan 0\left)\right)$

$=1$

Thus ${\int }_0^{\frac{\pi }{4}}se{c}^{2}xdx=1$