How Do You Evaluate an Integral Using Geometric Interpretation?

[Redbelly98]

That depends what the answer in back of your book is.
Remember that you need the integral of 3(4-x²)^1/2, not just (4-x²)^1/2

 

[Cyosis]

The question asked to interpret it in terms of area, that's why I didnt use any integration technique e.g. substitution, but instead tried to calculate in terms of half a circle (1/2 * pi * r^2). So is the answer at the back of my book wrong?

If you had read the post you quoted in #30 you would have known that the answer in the book is correct. I suggest you go back to the very start of the problem and look at the actual integral you're trying to calculate.

 

[Mentallic]

Just to sum it all up for you...

$$\int_{-2} ^{2} (x + 3)(4 - x^2)^{\frac{1}{2}} dx$$

Try expanding out (x+3)(4-x²)^1/2, then split the integral.


(Hint: (a+b)c = ac+bc)