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# Integrate the function $y\sin\left(x\right)$ from 0 to $2\pi$

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##  Step-by-step Solution 

Problem to solve:

$\int_{0}^{2\pi } y\sin\left(x\right)dx$

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Simplifying

$\int_{0}^{2\pi } y\sin\left(x\right)dx$

Learn how to solve definite integrals problems step by step online.

$\int_{0}^{2\pi } y\sin\left(x\right)dx$

Learn how to solve definite integrals problems step by step online. Integrate the function ysin(x) from 0 to 2*pi. Simplifying. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Apply the integral of the sine function: \int\sin(x)dx=-\cos(x). Evaluate the definite integral.

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##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int(ysin(x))dx&0&2*pi using basic integralsSolve int(ysin(x))dx&0&2*pi using u-substitutionSolve int(ysin(x))dx&0&2*pi using integration by partsSolve int(ysin(x))dx&0&2*pi using tabular integration

### Main topic:

Definite Integrals

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