Question

If $g\left(x\right)$ is the inverse of $f\left(x\right)$ and $f\left(x\right)$ has domain $x\in \left[1.5\right]$ where $f\left(1\right)=2$ and $f\left(5\right)=10$ then the values of ${\int }_1^{5}f\left(x\right)dx+{\int }_2^{10}g\left(y\right)dy$

• A. $48$
• B. $64$
• C. $71$
• D. $52$

Answer 1

The correct option is A $48$

It is given that $g\left(x\right)$ is the inverse function of $f\left(x\right)$ .

Therefore we can take the values of $f\left(x\right)$ and $g\left(x\right)$ as horizontal and vertical sides of the graph.

So, here the sum of the two limited integral referred in the question is-

The Area of the big rectangle – the Area of the smaller one $=10\times 5–2\times 1=50-2=48$