Area eh
The area of the shaded region can be written as , where and are positive coprime integers. Find .
The answer is 21.
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1 solution
The area of the shaded region is given by:
A = ∫ − 1 1 ( e y − y 2 + 3 ) d y = e y − 3 y 3 + 3 y ∣ ∣ ∣ ∣ − 1 1 = e − 3 1 + 3 − ( e 1 + 3 1 − 3 ) = 3 1 6 + e e 2 − 1
Therefore, a + b + c = 1 6 + 3 + 2 = 2 1 .