Question

Integration
The diagram shows the shaded region enclosed by the curve y=f(x) and a straight line y=2x.

Answer 1

\[Given~\int\limits_{0}^{k}f(x)~dx=13\]and the area od the shaded region is 4unit^2,find the value of k.

Answer 2

of*

Answer 3

@ganeshie8

Answer 4

Represent the area, as the difference of the area determined by the parabola, minus the one determined by the line:
\[\int\limits_{0}^{k}f(x)dx - \int\limits_{0}^{k}2xdx=4\]
now, the area of the parabola is given, which is \(\int\limits_{0}^{k}f(x)dx=13\) so therefore:
\[13-\int\limits_{0}^{k}2xdx=4\]
\[\int\limits_{0}^{k}2xdx=9\]
All you have to do know is calculate the integral on the left side and then solve the resulting expression for "k".

Answer 5

\[k=3\]

Answer 6

Thank you @Owlcoffee :)

Answer 7

no problem.