# Evaluate ∫ 1 0 ∫ X X 2 X Y ( X + Y ) D Y D X . - Applied Mathematics 2

Evaluate int_0^1 int_(x^2)^x xy(x+y)dydx.

#### Solution

We have,

I=int_0^1 int_(x^2)^x (x+y) dydx

I=int_0^1 [(x^2y^2)/2+(xy^3)/3]_(x^2)^x dx

I=int_0^1 [x^4/2+x^4/3-x^6/2-x^7/3]dx

I=[5/6.x^5/5-x^7/14-x^8/24]_0^1

I=1/6-1/14-1/24

I=3/56

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
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