20 Answered Questions for the topic Definite Integration

Definite Integration

03/14/18

#### estimating definite integral

absolute value of ∫(sinx)/(1+x8) from 10 to 19 is less than
10-10
10-11
10-7
10-9

Definite Integration Calculus

02/19/18

#### how to integrate √[ (1+y)/(1-y) ]dy from -1 to 0

integrate √[ (1+y)/(1-y) ]dy
from -1 to 0
the answer is: (pi/2) -1

02/11/18

#### What is ∫-7^-1 f(x)dx?

suppose that f(x) is an even function and let ∫0^1 f(x)dx = 5 and ∫0^7 f(x)dx = 1. What is ∫-7^-1 f(x)dx?
This is my work
I expand ∫-7^-1 f(x)dx to F(-1) - F(-7)
F(-1) - F(-7) is the...
more

#### What M value should I use? (how do i find it)

I was asked to calculate the area between two functions, y=e^x and y=x using midpoint riemann sums from 0-2 with n=4. so i found my answer by subtracting the second sum from the first.
The second...
more

Definite Integration

01/07/17

#### I need help to this problem!!

Integral of tan inverse of x divided by x, limits are from 1/2014 to 2014

#### If I have a spinning bowl of water...

A spinning liquid of any sort forms a paraboloid; a three dimensional parabolic shape. Therefore, you can apply the physics principles relating to centripetal motion to any mass, m, on the surface...
more

Definite Integration Integral Calculus

12/06/16

#### Find the interval [a,b] for which the value of the following integral is a maximum and explain the reasoning

∫ba (2+x-x2)dx

Definite Integration Integral Calculus

12/06/16

#### If f' is continuous on [a,b], show that

2∫ab f(x)f'(x)dx=[f(b)]2-[f(a)]2

#### Definite Integral with U-Substitution

I have an integral with ∫ (b=0, a=-1) and the inside function is (2t)/[(3+t2)3]dt. The directions tell me to "Evaluate the definite integral by making a u-substitution and integrating from u(a) to...
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Definite Integration Calculus

05/26/16

#### Definite integral question

Calculate the integral of:
cos [2x] π. cos πx dx
From 0 to 1.

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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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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#### 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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#### Cubic curve integral - area enclosing curve and x-axis

The curve is x^3-6x^2+11x-6. I have to prove that the two regions enclosed between the x-axis and the curve are equal. Given is, that the curve cuts the x-axis at x=1,x=2 and x=3. I tried finding...
more

#### Express limit as definite integral?

limit as n goes to infinity.
n
Σ i4/n5 on interval [0,1]
i=1
Options are:
1 1 1 7 1
∫ 1/x5 , ∫ 1/x4 , ∫ x4 , ∫ x5 ...
more

Definite Integration

06/01/15

#### how do the constants of integration cancel out during definite integration

how do the constants of integration cancel out during definite integration.
please answer these.

#### Definite Intergrals

Approximate the area of the region bounded by the graph of f(x)= cos (t/2-7pi/8) and the t-axis on [7pi/8, 15pi/8] with n=4 sub intervals. Use the midpoint of each sub interval to determine the...
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Definite Integration

07/23/14

#### Calculus question

Find each definite integral
top:3 bottom:0 (square root) y+1dy
top:3 bottom:2 1/e^x Dx

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