definite integrals

Question

 

If a​ = 14​, then find the value of   ∫−a3af(x) dx.

  

ROUND YOUR FINAL ANSWER TO 4 DECIMAL PLACES.

∫−a3af(x) dx ≈ ___ 

Answer 1

Hi, if the problem is in the context of the linked problem from the comment section, then you can solve this question using geometric shapes.

The integral of f(x) from -a to a is a semicircle with radius a, which means the area is 0.5*pi*a^2=0.5*pi*(14)^2=98pi.

Then, since the second part of the function is all under the x-axis, the area under will subtract from the first value. The area under the graph is a triangle and a square with a total area of 3/2a^2 or 3/2*(14)^2=294.

Now, we can type our answer: 98pi-294.