166 Answered Questions for the topic Integration

05/25/16

#### Integral limit definition

No limit is visible in integral notation, but integration is defined in terms of a limit. Give the definition; explain what is being limited, and how this allows an integral to calculate the exact...
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Integration

05/24/16

#### Integration breaking down? Or am I being thick?

So 1/5 / P is the same as 1/5P however they integrate to 1/5lnP and 1/5ln5P respectively, what's with this differnence?

#### I know the two endpoints on a curve and I know the area under the curve but I do not know the function of the curve. How can I find the function of the curve?

The integral from 0 to 27 of f(x)dx is 0.46896. I need to know what the function for f(x) is.
The two endpoints of the curve are (0,0) and (27,0.2894).

05/06/16

#### A PDF is given by formula p(x)=2e^(-2x),x>0. Determine P(X>1).?

A PDF is given by formula p(x)=2e^(-2x),x>0. Determine P(X>1).? PDF being Probability Density Function
A PDF is given by formula p(x)=2e^(-2x),x>0. Determine P(X>1).?

Integration Calculus

05/02/16

#### Calculus Integration Problem 2

A stone is dropped from the edge of a roof, and hits the ground with a velocity of −180 feet per second. Assume the acceleration due to gravity is -32 feet per second squared. How high (in feet) is...
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Integration Calculus

05/02/16

#### Calculus Integration Problem

A stone is thrown straight down from the edge of a roof, 900 ft above the ground, at a speed of 7 ft/sec.
A. Given that the acceleration due to gravity is -32 ft/sec2, how high is the stone 2...
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Integration Integral Calculus

04/30/16

#### Finding the integral

Let F(x) = ∫eu^2 + cos(u) du with upper limit = 7x, lowerlimit = 0
Compute F'(0)
I have no idea how to approach this question the 7x in the upper limit is quite off putting

#### Integration question involving cosh^-1???

Evaluate the integral (1/sqrt(x^2 - 5))dx on limits of 3 to 4, using the formula: integral of (1/sqrt(x^2 - a^2))dx.
Recall that this formula was found by using the substitution x = a cosh t, and...
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Integration

04/27/16

#### integral of dx/(50-10x)

If ∫dx/(50-10x)=1/10∫dx/(5-x)
∫dx/(50-10x)
u=50-10x du=-10dx dx=du/-10 -1/10∫du/u=-1/10ln[50-10x]+c
1/10∫dx/(5-x)
u=5-x du=-1dx dx=-du -1/10∫du/u=-1/10ln[5-x]+c
If the...
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04/23/16

#### integration

show that ∫dx/(2+3sinx) [upper limit pi/2, lower limit 0] = ∫dt/((t+ 3/2)2 - (√5/2)2) [ upper limit 1, lower limit 0]
I know that sin(x) = 2t/(t2+1), where t = tan(x/2) but i cannot get the...
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Integration Substitution Method

04/22/16

#### Integration by Substitution

Find using substitution:
∫ 1/[x(1+lnx)2] dx
I'm not sure what substitution to use.

04/22/16

#### PROFIT FUNCTION IN CALC

I need help answering this word problem...I need to find the function P(t) and I just can't remember the process whatsoever
"A company has its profit function P(t) defined since its inception...
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#### Indefinite Integral

Can someone help me solve for this indefinite integral?:
(u^2 + u)/(2u^3 + 3u^2 + 1)^(2/3)
Thank you!

#### Indefinite/Definite Integrals

I need help solving a couple of indefinite/definite integrals. It seems all of my homework problems have done the less complicated ones so I'm not sure how to do these ones:First problem:...
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Integration Differentiation

04/09/16

#### Show sin(x) is less than or equal to x

Show that sin(x)≤x for all x≥0 (hint look at the derivative of x-sin(x))

#### Physics calculus

the initial velocity of a particle is u and the acceleration is given by a=kt, where k is a positive constant. the distance travelled in time t is

Integration Calculus 3

12/04/15

#### Integrate f(x,y,z)=x over the region bounded above by z=4-x^2-y^2 and below by z=x^2+3y^2

Im really stuck on this one. If anyone could tell me how to do this and the answer that would be great!
Integrate f(x,y,z)=x over the region bounded above by z=4-x^2-y^2 and below by z=x^2+3y^2

Integration Antiderivative

12/01/15

#### fint antiderivatives!

Find all antiderivatives of y=e^x-2x^3+1/5x

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