Question

Find the area of the region that lies under the curve y = x^2 and above the x-axis for x between 0 and 1.

Answer 1

Answer:

Step-by-step explanation:

To find area of curves we use the process of definite integration

given = y= x^2

$\int\limits^1_0 {x^{2} } \, dx$

Integrating $x^{2}$ with respect to x

we get

$\frac{ x^3}{3}$

ANd now finally putting the limits

$\frac{(1)^3}{3} - \frac{(0)^3}{3}$

Hence your answer should be 1/3

hope you got it mate

:)

Answer 2

ANSWER :-

To find area of curves we use the process of definite integration

$\tt\green{given = y= x²}$

$\int\limits^1_0 {x^{2} } \, dx$

1

∫ x²dx

0

Integrating $\begin{lgathered}x^{2} \\\end{lgathered}$with respect to x

we get

$\frac{x^3}{3}$

ANd now finally putting the limits

$\begin{lgathered}\frac{(1)^3}{3} - \frac{(0)^3}{3}\\\end{lgathered}$

Hence your answer should be $\frac{1}{3}$

hope you got it mate

:)