** Final answer to the problem

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** Step-by-step Solution **

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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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We can solve the integral $\int_{0}^{1}\cos\left(\frac{\pi }{2}x\right)dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. We see that $\frac{\pi }{2}x$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

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

$u=\frac{\pi }{2}x$

Learn how to solve definite integrals problems step by step online. Integrate the function cos(pi/2x) from 0 to 1. We can solve the integral \int_{0}^{1}\cos\left(\frac{\pi }{2}x\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \frac{\pi }{2}x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify.

** Final answer to the problem

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