Question

Let for $x \in R$ $f(x)=\frac{x+|x|}{2} \text { and } g(x)=\begin{cases}x, & x<0 \\\x^2, & x \geq 0\end{cases}$

Then area bounded by the curve $y=(f \circ g)(x)$ and the lines $y=0,2 y-x=15$ is equal to

Answer 1

The correct answer is 72.

2y−x=15
A=0∫3​(2x+15​−x2)dx+21​×215​×15
4x2​+215x​−3x3​∣∣​03​+4225​
=49​+245​−9+4225​=499−36+225​
=4288​=72