2∫ab f(x)f'(x)dx=[f(b)]2-[f(a)]2

2∫ab f(x)f'(x)dx=[f(b)]2-[f(a)]2

I still havent learned anthing about logarithm derivatives yet so i have no idea how to proof this even i know the answer is ln2. So far with the definition of integral i transformed...

∫ba (2+x-x2)dx

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places. y=x^2+4, y=6x-6; -1 <x<2

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...

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

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...

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:...

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),...

Use the substitution u = x - 1/x to show that the integral from 1 to (√pi +√2)/2...

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...

definite integral question

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

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

integrate from pi/6 to pi/2 (x+16/(sinx^2))dx

There was a direct formula for this in definite integrals but i don't know how they evaluated it?

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 height...

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

Xinran W.

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Marianna L.

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