20 Answered Questions for the topic Definite Integration

Definite Integral Evaluation

∫30 x2 Sqrt(x+1) dx ?

estimating definite integral

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

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

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

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

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... more

Definite integral question

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

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


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

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

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

integrate 0 to pi/2 xsinx/1+ cos2x

definite integral question

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

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... more

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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