The area of the region bounded by the curve $y=4 x^{3}-6 x^{2}+4 x+1$ and the lines $x=1, x=5$ and $x$ axis is

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Aicharya · Accepted Answer

Required area is shaded. $\begin{array}{l} \int_{1}^{5} 4 x^{3}-6 x^{2}+4 x+1 d x \ =\left[\frac{4 x^{4}}{4}-\frac{6 x^{3}}{3}+\frac{4 x^{2}}{2}+xight]_{1}^{5} \ =\left[x^{4}-2 x^{3}+2 x^{2}+xight]_{1}^{5} \ =\left[5^{4}-2(5)^{3}+2(5)^{2}+5ight]-\left[1^{4}-2(1)^{3}+2(1)^{2}+1ight] \ =[625-250+50+5]-[1-2+2+1] \ =430-2=428 	ext { sq. units } \end{array}$

The area of the region bounded by the curve $y=4 x^{3}-6 x^{2}+4 x+1$ and the lines $x=1, x=5$ and $x$ axis is

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