20 Answered Questions for the topic Definite Integration

08/08/18

Definite Integral Evaluation
∫30 x2 Sqrt(x+1) dx ?
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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
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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
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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
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07/11/17

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
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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
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12/26/16

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
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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
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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
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06/23/16

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... more
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05/26/16

Definite integral question
Calculate the integral of:  cos [2x] π. cos πx dx From 0 to 1.
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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... more
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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... more
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04/21/16

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:... more
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02/02/16

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
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11/25/15

integrate 0 to pi/2 xsinx/1+ cos2x
definite integral question
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07/17/15

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
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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.
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11/10/14

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... more
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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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