Warm up problem 13: exponential area medium

Calculus Level 3

In the graph above, the area of the green shaded section contained beneath the red line x + 1 \sqrt{x+1} and above the x-axis and above the blue line x \sqrt{x} from x=-1 to x=2 Can be represented as a b − c d e a\sqrt b-\dfrac{c\sqrt d}{e} where b,d are square free and c,e are coprime. Find a + b + c + d + e a+b+c+d+e .


The answer is 14.

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Trevor Arashiro by Trevor Arashiro , 22, USA

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1 solution

Aya Alaa
Oct 10, 2014

∫ − 1 2 ( x + 1 ) 1 2 d x − ∫ 0 2 x 1 2 d x \int_{-1}^2 (x+1)^{\frac{1}{2}} dx-\int_0^2 x^{\frac{1}{2}} dx

= 2 3 − 4 2 3 =2\sqrt3-\dfrac{4\sqrt2}{3}

then a + b + c + d + e = 2 + 3 + 4 + 2 + 3 = 14 a+b+c+d+e=2+3+4+2+3=14

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Trevor Arashiro - 6 years, 8 months ago

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thanks @Trevor Arashiro

Aya Alaa - 6 years, 8 months ago

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