Area Under the Curve
Area Under a Curve
Premium Question
Grade 12
Question:
The area bounded by the curve $y = \cos x$, the $x$-axis, $x = 0$ and $x = \frac{\pi}{2}$ is:
(1) $1$
(2) $\frac{\pi}{2}$
(3) $2$
(4) $\frac{1}{2}$
Step-by-Step Solution
Key Concept: Recall that $\cos x \geq 0$ throughout $[0, \pi/2]$, so the area is simply $\int_0^{\pi/2} \cos x \, dx$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)