Integrate
-$\int _ { 0 } ^ { 1 } \sec ^ { 2 } \left( \frac { \pi x } { 4 } \right) d x$
A) $\frac { 4 } { \pi }$
B) - $\frac { \pi } { 4 }$
C) $\frac { \pi } { 2 }$
D) $\frac { \pi } { 4 }$
E) none of these

Question

Quizplus · Accepted Answer

The integral of $\sec^2(ax)$ is $\frac{1}{a}\tan(ax) + C$. Applying this to the given integral, we get $\frac{4}{\pi}\tan\left(\frac{\pi x}{4}\right)$ evaluated from 0 to 1, which simplifies to $\frac{4}{\pi}$.

Integrate - ∫01sec⁡2(πx4)dx\int _ { 0 } ^ { 1 } \sec ^ { 2 } \left( \frac { \pi x } { 4 } \right) d x∫01​sec2(4πx​)dx

Integrate
- $\int _ { 0 } ^ { 1 } \sec ^ { 2 } \left( \frac { \pi x } { 4 } \right) d x$