Explore BrainMass

Explore BrainMass

    Integration and Fundamental Theorem Calculus

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Question 1
    Find
    ∫ x3+4
    ________________________________________x2 dx

    Question 2

    Apply the Fundamental Theorem of Calculus to find the derivative of:
    h(x)= x∫2^/¯u-1dx

    Question 3

    Evaluate:
    ∫2cos2 xdx

    © BrainMass Inc. brainmass.com December 24, 2021, 7:21 pm ad1c9bdddf
    https://brainmass.com/math/integrals/integration-fundamental-theorem-calculus-182045

    Attachments

    SOLUTION This solution is FREE courtesy of BrainMass!

    The solution file is attached.

    Question 1
    Find
    ∫ x3+4
    ________________________________________x2 dx

     (x^3 + 4)dx /x^2 =  (x^3 /x^2) dx + 4/(x^2) dx =  x dx + 4  (1/x^2)dx
    = x^2 /2 - (4/x) + C

    Question 2

    Apply the Fundamental Theorem of Calculus to find the derivative of:
    h(x)= x∫2^/¯u-1dx

    I am not sure how to interpret the integral here. Let me do it in two different ways ...
    (a)  [Öu - 1]dx =  Öu dx -  dx = Öu * (x) - x + C = x(Öu - 1) + C
    On applying the limits, we get the integral as x(Öu - 1) - 2(Öu - 1) = (Öu - 1)(x - 2)
    (b)  Ö(u - 1) dx = Ö(u - 1)  dx = [Ö(u - 1)] x + C
    On applying the limits, we get the integral as [Ö(u - 1)](x - 2)

    Question 3

    Evaluate:
    ∫2cos2 xdx

     2 cos^2 x dx =  (1 + cos 2x) dx =  dx +  cos 2x dx = x + (1/2) sin 2x + C.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:21 pm ad1c9bdddf>
    https://brainmass.com/math/integrals/integration-fundamental-theorem-calculus-182045

    Attachments

    ADVERTISEMENT