Find the total area of the region between the curve and the x-axis.
-$$\mathrm { y } = \mathrm { x } ^ { 2 } + 1 ; 0 \leq \mathrm { x } \leq 1$$
A) $\frac { 4 } { 3 }$
B) $\frac { 5 } { 3 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 1 } { 3 }$

Question

Quizplus · Accepted Answer

The area between the curve and the x-axis is given by the integral of the function from x = 0 to x = 1.$$\int_0^1 (x^2 + 1) dx = \left[\frac{x^3}{3} + x\right]_0^1 = \frac{1}{3} + 1 = \frac{4}{3}$$

Find the Total Area of the Region Between the Curve y=x2+1;0≤x≤1\mathrm { y } = \mathrm { x } ^ { 2 } + 1 ; 0 \leq \mathrm { x } \leq 1y=x2+1;0≤x≤1

Find the Total Area of the Region Between the Curve $\mathrm { y } = \mathrm { x } ^ { 2 } + 1 ; 0 \leq \mathrm { x } \leq 1$