Question

Let $y=g(x)$ be the inverse of a bijective mapping $f: R \rightarrow R f(x)=3 x^3+2 x$. The area bounded by the graph of $g(x)$, the $x$-axis and the ordinate at $x=5$ is :

• A. $\frac{5}{4}$
• B. $\frac{7}{4}$
• C. $\frac{9}{4}$
• D. $\frac{13}{4}$

Answer 1

Answer: (D)

note for inverse function $y$ axis will be the $x$ axis and $x$ axis will be the $y$ axis
$\text { required area } =\text { Area of rectangle }-\int\limits_0^1 f(x) d x $
$ =5-\int\limits_0^1\left(3 x^3+2 x\right) d x $
$=5-\left(\frac{3}{4}+1\right)=3 \frac{1}{4}=\frac{13}{4} $