Find the value of the integral $\int _ { 0 } ^ { 1 } ( x + 1 ) ^ { 2 } d x$
A)$\frac { 7 } { 3 }$

B)0
C)1
D) $\frac { 5 } { 3 }$
E)2
F) $\frac { 1 } { 3 }$

G) $\frac { 4 } { 3 }$

H) $\frac { 2 } { 3 }$

Question

Find the value of the integral $\int _ { 0 } ^ { 1 } ( x + 1 ) ^ { 2 } d x$ 
A)$\frac { 7 } { 3 }$

B)0
C)1
D) $\frac { 5 } { 3 }$ 
E)2
F) $\frac { 1 } { 3 }$

G) $\frac { 4 } { 3 }$

H) $\frac { 2 } { 3 }$

Quizplus · Accepted Answer

Expanding $(x + 1)^2$ gives $x^2 + 2x + 1$. Integrating term by term from 0 to 1, we get $\frac{1^3}{3} + \frac{2(1^2)}{2} + 1 = \frac{1}{3} + 1 + 1 = \frac{7}{3}$.

Find the Value of the Integral ∫01(x+1)2dx\int _ { 0 } ^ { 1 } ( x + 1 ) ^ { 2 } d x∫01​(x+1)2dx

Find the Value of the Integral $\int _ { 0 } ^ { 1 } ( x + 1 ) ^ { 2 } d x$