Find 'a' if the area enclosed by f(x), x-axis and x=a is 18. Refer the image below.

Hi, I don't know what should i do. Can anyone help me.

Thanks.

Question

Find 'a' if the area enclosed by f(x), x-axis and x=a is 18. Refer the image below.

Hi, I don't know what should i do. Can anyone help me.

Thanks.

rahulmr · Answer

attachment

arthur326 · Answer

We have $\displaystyle\int_0^a f(x) \, dx = 18$. You should be able to solve for $a$ by evaluating the integral on the left-hand side.

arthur326 · Answer

At least that's what the figure makes it look like, since the function is not drawn for $x<0$. The question you typed though does not specify that $x=0$ is an extremity.

rahulmr · Answer

Thanks for the help @arthur326

rahulmr · Answer

I got 2 and -2 for the answer and since a>0, the answer must be 2.

arthur326 · Answer

$a=2$ checks out, if we're finding the area as in the figure. I'm guessing the $y$-axis was meant to be a boundary also, for if it wasn't we'd have to integrate from one of the roots of the function.