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Evaluate the integral. $ \displaystyle \int_0^…
06:46

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Problem 25 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int_0^1 \frac{1 + 12t}{1 + 3t}\ dt $

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Related Courses

Calculus 2 / BC
Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Related Topics

Integration Techniques

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Top Calculus 2 / BC Educators
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Video Thumbnail

01:53
Integration Techniques - Intro

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.
Video Thumbnail

27:53
Basic Techniques

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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Watch More Solved Questions in Chapter 7

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Problem 16
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Problem 84

Video Transcript

because we have polynomial divided by polynomial and they're both too The first power I would go ahead and do long division here, so go using the polynomial division to simplify the inside weaken right. This is for that's the kosher. Remainder is negative three and then we have one plus bt on the bottom. So So this is from using just doing the polynomial division and then you can see our new integral is easier than the original. So the internal afore we know that she's fourteen here. If this three in front of the T and this plus one is bothering you, you can go ahead and use the use up here, from which you can see that do you equals three dt So I won't write out the full details there. But if this may help you integrate, then we have minus three natural log one plus three tea and then we'LL also have to divide by three due to this in the use of our end point zero one and then cross off those threes. So plug in the one first for tea, we just get a four and then plug it into the natural line your natural log before. And then when you plug in zero for tea both. Herms Laura zero. So that's your final answer.

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Related Topics

Integration Techniques
Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53
Integration Techniques - Intro

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.
Video Thumbnail

27:53
Basic Techniques

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