Use geometry to find the exact value of $\int _ { 0 } 2 + \sqrt { 9 - x ^ { 2 } } d x$
A) $\frac { 6 + 81 \pi } { 2 }$
B) $\frac { 6 + 9 \pi } { 4 }$
C) $\frac { 6 + 81 \pi } { 4 }$
D) $\frac { 24 + 9 \pi } { 4 }$

Question

Quizplus · Accepted Answer

The integral can be split into two parts: $\int_0^2 2 \, dx$ and $\int_0^2 \sqrt{9 - x^2} \, dx$. The first part is a rectangle with area 4. The second part is a quarter-circle with radius 3, but only from 0 to 2, so its area is $\frac{1}{4} \times \frac{9\pi}{2}$. Adding these gives $\frac{24 + 9\pi}{4}$.

Use Geometry to Find the Exact Value Of ∫02+9−x2dx\int _ { 0 } 2 + \sqrt { 9 - x ^ { 2 } } d x∫0​2+9−x2​dx

Use Geometry to Find the Exact Value Of $\int _ { 0 } 2 + \sqrt { 9 - x ^ { 2 } } d x$