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# Find the area under the given curves and given lines: $(ii)\:y = x^4, x = 1, x = 5 \: and\: x - axis$

This is second part of multipart q1

Toolbox:
• Area of a region bounded by the curve $y=f(x)$,$x$-axis and the lines $x=a,x=b$ is given by $A=\int_a^b dA=\int_a^b yda=\int_a^bf(x)dx.$
Step 1:
Given :
$f(x)=x^4,a=1;b=5$
since $A=\int_a^bf(x)dx$
substituing for $f(x),a$ and $b$ we get,
$A=\int_1^5x^4.dx=\begin{bmatrix}\large\frac{x^5}{5}\end{bmatrix}_1^5$
Step 2:
Applying the limits we get,
$=\begin{bmatrix}\frac{5^5}{5}\end{bmatrix}-\begin{bmatrix}\frac{1^5}{5}\end{bmatrix}=\large\frac{3125-1}{5}=\frac{3124}{5}$
Hence the required area is 624.8sq.units.