Evaluate the double integral ∬D(x2+6y)dA, where D is bounded by y=x, y=x3, and x≥0.

Answer 1

x³ = x; x = 0, x = 1

∫∫_D(x² + 6y)dA = ∫₀¹dx∫_x^3^x(x² + 6y)dy = ∫₀¹(x²y + 3y²)_x^3^xdx = ∫₀¹(x³ + 3x² - x⁵ - 3x⁶)dx = 1/4 + 1 - 1/6 - 3/7 =

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