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Popular >

integral of 2ysin(x)

Solution

\int 2 y sin (x) d y

Solution

y^{2} sin (x) + C

Solution steps

\int 2 y sin (x) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 sin (x) \cdot \int y d y

Apply the Power Rule

: \frac{y ^{2}}{2}

= 2 sin (x) \frac{y ^{2}}{2}

Simplify

2 sin (x) \frac{y ^{2}}{2} : y^{2} sin (x)

= y^{2} sin (x)

Add a constant to the solution

= y^{2} sin (x) + C

Popular Examples

(dy)/(dx)=(1+x)(1+y)

\frac{d y}{d x} = (1 + x) (1 + y)

integral of (e^{-x}sin^2(x))/2

\int \frac{e ^{- x} sin ^{2} ( x )}{2} d x

limit as x approaches 0 of (sin(x))/(4x)

x \to 0 lim (\frac{sin ( x )}{4 x})

derivative of Ae^{3x}+3Axe^{3x}

\frac{d}{d x} (A e^{3 x} + 3 A x e^{3 x})

limit as x approaches 1 of 4x^5-2x^4-3

x \to 1 lim (4 x^{5} - 2 x^{4} - 3)

Frequently Asked Questions (FAQ)

What is the integral of 2ysin(x) ?
The integral of 2ysin(x) is y^2sin(x)+C