Find the area under the curve y = sin 2x from x = 0 to x = $\frac { \pi } { 4 }$ .
A) 0
B) $\frac { 4 \pi } { 3 }$
C) -1
D) $\frac { 1 } { 2 }$
E) none of these

Question

Quizplus · Accepted Answer

The area under the curve y = sin 2x from x = 0 to x = $\frac{\pi}{4}$ is found by integrating the function: $\int_{0}^{\frac{\pi}{4}} \sin(2x) \, dx$. The antiderivative of sin(2x) is $-\frac{1}{2} \cos(2x)$. Evaluating from 0 to $\frac{\pi}{4}$, we get $-\frac{1}{2}[\cos(\frac{\pi}{2}) - \cos(0)] = -\frac{1}{2}[0 - 1] = \frac{1}{2}$.

Find the Area Under the Curve Y = Sin 2x π4\frac { \pi } { 4 }4π​

Find the Area Under the Curve Y = Sin 2x $\frac { \pi } { 4 }$