Find the value of the integral $\int _ { 0 } ^ { 1 } \sqrt { 1 - u ^ { 2 } } d u$
A)2
B)1
C) $\frac { \pi } { 4 }$
D) $\frac { 1 } { 4 }$
E) $\frac { 1 } { 2 }$
F) $\pi$
G) $\frac { \pi } { 2 }$
H) $2 \pi$

Question

Find the value of the integral $\int _ { 0 } ^ { 1 } \sqrt { 1 - u ^ { 2 } } d u$ 
A)2
B)1
C) $\frac { \pi } { 4 }$ 
D) $\frac { 1 } { 4 }$ 
E) $\frac { 1 } { 2 }$ 
F) $\pi$ 
G) $\frac { \pi } { 2 }$ 
H) $2 \pi$

Quizplus · Accepted Answer

The integral $\int _ { 0 } ^ { 1 } \sqrt { 1 - u ^ { 2 } } d u$ represents the area of a quarter circle with radius 1. The area of a full circle with radius 1 is $\pi r^2 = \pi$, so a quarter of this area is $\frac{\pi}{4}$.

Find the Value of the Integral ∫011−u2du\int _ { 0 } ^ { 1 } \sqrt { 1 - u ^ { 2 } } d u∫01​1−u2​du

Find the Value of the Integral $\int _ { 0 } ^ { 1 } \sqrt { 1 - u ^ { 2 } } d u$