Question

Fig. shows the curve y = x2. Find the area of
the shaded part between x = 0 and x = 6.
​

Answer 1

Answer:

See below.

Explanation:

We have the function,

$f( x ) = x^2$

Integration with respect to variable x,

$\int f(x) \ dx = \frac{x^3}{3}$

Let's call this function g( x ), so,

$g( x ) = \frac{x^3}{3}$

The definite integration will be,

$\int\limits^6_0 f(x)} \ dx= g( 6 ) - g( 0 )$

On solving we get,

$= g( 6 ) - g( 0 )\\= g ( 6 )\\= 72$

The area is 72 square units.