175 Answered Questions for the topic Integration


How do you tell when an improper integral converges or diverges? (specific question)

Hello! I'm having trouble understanding why the improper integral I'm answering is labeled as divergent when it looks like it converges. The improper integral is 1/x3, in-between the interval [-1,... more
Integration Math Calculus Volume


Application of Integration. Finding Volume: Rotating the region.

I need a tutor's assistance on a homework problem. I am given y=x^2, x=y^2, and about y=1. And I am asked to find the volume by rotating the region bounded by the given curves about y=1. However, I... more
Integration Math Calculus Calc


Finding area of a region on graph using integration.

Consider the following.y = x2y = 12 − x(a) Find the area of the region by integrating with respect to x.(b) Find the area of the region by integrating with respect to y.Any help will be very... more
Integration Calculus


Find the area of the region bounded by y=1/x^2, y=4, and x=5. Use any method to solve.(e.g washer, disk shell)

Use any method listed above.


indefinite integral using partial fractions


find the indefinite integral by using partial fractions



What is the right hand riemann sum approximation

A function f is continuous on the closed interval [4,12] and differentiable on the open interval (4,12) and f has the values below. Using 4 subintervals, what is the right hand riemann sum... more
Integration Calculus


Use integration by substitution to solve the integral below. Use the C for the constant integration.

f(sqrt 3x^4-4x+3)(12x^3-4)dxPlease help. I can send a picture of the equation if it’s confusing.
Integration Calculus


calculus functions integration by parts

Which of the following functions of x can be integrated with respect to x without integration by parts, and purely using integration by u-substitution and the knowledge of the antiderivative of the... more
Integration Calculus


Calculus Integration by Parts

Which of these integrals requires the method of integration by parts? (4 points)Answer Choices:
Integration Calculus Derivatives


Differentiation and Integration of a difficult function

I am an expert and experienced Math and Physics professional. I thought I could use help from Math tutoring community and new ideas for solution of a difficult problem.∫.Given that y =... more

Maclaurin Series Term by Term Integration

Approximate the integral from 0 to 1 of (sin(x)/x) dx with an accuracy of 10^-6 using the Maclaurin series of sin, division of that Maclaurin series by x, and term-by-term integration. You will... more


Maclaurin Series and Term-By-Term Integration

Approximate the integral from 0 to 1 of e^(-x^2)dx with an accuracy of 10^-6 using the maclaurin series of e^x , replacement of x by -x^2, and term-by-term integration. You will have to figure out... more


Maclaurin Series and Term-by-term Integration


Maclaurin Integration and Term-by-Term Integration

1.)a-Evaluate the integral from 0 to 1/2 of ln(1+x)dx with an accuracy of 10^-4 using techniques of integration and a calculator.b- Now approximate the integral from 0 to 1/2 of ln(1+x)dx to an... more

Trigonometric Substitution Integration

4.) ∫((9-25x^2)^(1/2)*dx)/(x^2)


Trigonometric Substitution Integration

3.) ∫(dx)/((x)*(9+25x^2)^(1/2))


Trigonometric Substitution Integration

2.) ∫ ((9+25x^2)^(1/2)*dx)/(x^2)


Trig Substitution Integration


Fundamental theorem of Calculus

Given that D(t) is a continuous and diffrentiable function . Also D(0) = 0 , D(5) = 120 and D(20) = 200 , simplify the integral using fundamental theorem , ∫ D'(t/4)dt inthe interval 0<t... more
Integration Calculus Calculus 2


Calculus Question HEEELP!!

Let, x^2f(x) = ∫ e^(-t^2) dt xfind the critical points of f(x) WITH DETAILS . note: integral from (x) to (x^2).
Integration Calculus Calculus 2



If f is integrable on [a, b], show by example that : tF (t) = ∫ f(x) dx ais continuous but need not to be differentiable.note: the integral from (a) to (t).
Integration Calculus Calculus 2



Definition: A function p (t) is a probability density function provided it satisfies the following properties:1. p (t) >= 0 for all t,2. integral from (negative infinity ) to ( infinity) of p(t)... more

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