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  4. If the area enclosed by g(x), x=-3, x=5 and x-axis where g(x) is the inverse of f(x)=x3+3 x+1 is A, then [A] equals [Note: [k] denotes the greatest integer function less than or equal to k.]

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Q. If the area enclosed by $g(x), x=-3, x=5$ and $x$-axis where $g(x)$ is the inverse of $f(x)=x^3+3 x+1$ is $A$, then $[A]$ equals
[Note: [k] denotes the greatest integer function less than or equal to $k$.]

Application of Integrals

Solution:

image
Area $=\int\limits_{-1}^0\left(\left(x^3+3 x+1\right)-(-3)\right) d x+\int\limits_0^1\left(5-\left(x^3+3 x+1\right)\right) d x=\frac{9}{2}$