Question

Find the area under given curves and given lines.

(a) $y=x^2;x=1,x=2$ and X - axis (b) $y=x^4;x=1,x=5$ and X - axis.

Answer 1

The given curve $y=x^2$ represents an upward parabola with vertex (0, 0) and axis along Y - axis.

$\therefore$ Required area (shown in shaded region)

= Area under the curve $y=x^2$,

X - axis and x = 1, x = 2

$={\int }_1^5{x}^{4}dx=[\frac{x^5}{5}{]}_1^5=\frac{1}{5}[5^5-1]=\frac{1}{5}(3125-1)=\frac{3124}{5}=624.8squnit$