Explore BrainMass

Explore BrainMass

    Fundemental Theorm of Calculus : Integrals and Areas (8 Problems)

    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!

    Find the area of the region

    1.) y=x- x^2 points (0,1/4) (1,0)

    2.) y=1/x^2 points ((1,1) (2, 1/2)

    Find and evaluate the integral

    1.) integral 1 to 0 2xdx

    2.) integral 0 to -1 (2x +1)dx

    3.) integral 1 to -1 (2t -1)^2 dt

    4.) integral 5 to 2 (-3x +4) dx

    5.) integral 4 to 0 1/sq rt 2x +1 dx

    6.) integral 2 to 0 x/ sq rt 1+2x^2 dx.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:18 pm ad1c9bdddf
    https://brainmass.com/math/integrals/fundamental-theorem-calculus-integrals-areas-39546

    Solution Preview

    1.) y = x - x^2

    points (o,1/4) (1,0)

    Area under the curve y=f(x) and the points x=a and x=b is given by

    A = Int ydx with the limit from a to b

    Here, A = Int (x - x^2 ) from 0 to 1

    A = x^2/2 - x^3/3 Applying limits, ==> 1^2/2 - 1^3/3 - 0 = 1/2 - 1/3 = 1/6 --ans

    2.) y=1/x^2

    points ((1,1) (2, 1/2)

    similarly, A = Int(1/x^2) limit from x = 1 to x=2

    = -1/x applying limits

    = ...

    Solution Summary

    Eight integrals and areas are found and the details are discussed in the solution.

    $2.49

    ADVERTISEMENT