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Evaluate the integral.

$ \displaystyle \int_0^1 (3x + 1)^{\sqrt{2}}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Harvey Mudd College

Baylor 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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Evaluate the indefinite in…

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Find the Integral of \int …

Let's evaluate the given in several here, we should take you to be three x plus one. So this is using They use up, then do you? Over three. It's the X. So here we can rewrite this in overall. So watch out for these limits of integration. So plug in X equals zero We ate you equals one and then plugging in X equals one gives you eagles for so that's the upper bound. Then we know that we're supposed to have a one over three year from this from the use up, and then they're so here in parentheses. That's just you. And now we raise that to the swearing to power. So now, to do this in a girl, just use the power rule. So we add one to the exponents, and then we divide by the exponents and then plugging your end points and subtract. So again, four Route two plus one minus one all over this and that's your final answer.

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