Exercise
$\int_0^1\left(5xy\sqrt{x^2+y^2}\right)dy$
Step-by-step Solution
Learn how to solve special products problems step by step online. Integrate the function 5x(yx^2+y^2)^(1/2) from 0 to 1. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. We can solve the integral \int\sqrt{yx^2+y^2}dy by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dy, we need to find the derivative of y. We need to calculate dy, we can do that by deriving the equation above.
Integrate the function 5x(yx^2+y^2)^(1/2) from 0 to 1
Final answer to the exercise
$5x\left(\frac{1\sqrt{yx^2+1^2}+yx^2\ln\left|\frac{\sqrt{yx^2+1^2}+1}{yx}\right|}{2}-\frac{0\sqrt{yx^2+0^2}+yx^2\ln\left|\frac{\sqrt{yx^2+0^2}+0}{yx}\right|}{2}\right)$