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Evaluate the definite integral.$\int_{0}^{1} \cos (\pi t / 2) d t$

$\frac{\sqrt{2}}{\pi}$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Missouri State University

Campbell University

Oregon State University

Idaho State University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

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Evaluate the integral.…

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Evaluate the definite inte…

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here. This question tells us to evaluate the definite integral First stop as we know that we can use U substitution or use what's in parentheses. Therefore, our DT is to over pi. Do you? Therefore we can pull out the two over pie because it's a constant. We have two over pi times The intro from zero to pi over too co sign of you. Do you? We know the integral of coastline of you is a sign of you, which means we can now plug n member were always doing our upper bound minus or lower bound. That's very important. The order matters because you've got a different answer. Otherwise, this is equivalent to squirt of two divided by pi.

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