Explore BrainMass

Explore BrainMass

    Integration using left, right, trapezoid, and midpoint rules

    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!

    (See attached file for full problem description)

    Definite integrals
    1. Show geometrically why int sqrt (2-x^2) dx = pi/4 + 1/2
    2. Approximate int sqrt (2-x^2) dx for n = 5 using the left, right, trapezoid, and midpoint rules. Compute the error in each case using the answer to question 1 to compare the errors

    © BrainMass Inc. brainmass.com September 27, 2022, 10:36 am ad1c9bdddf
    https://brainmass.com/math/integrals/integration-using-left-right-trapezoid-midpoint-rules-67478

    Attachments

    Solution Preview

    Please see the attached file.

    1.
    Show geometrically why .

    This is an equation of a circle with radius sqrt 2 as shown above.

    The given integral is the area of the circle from x = 0 to x = 1 in the first quadrant . I have shaded this area in the first diagram.

    Therefore the value of the integral = Area of the shaded region.

    We will find this area using geometry. We need to find area ODAC.

    Area ODAC =Area OBC - Area of OAB + Area of OAD(this is a ...

    Solution Summary

    Very detailed solutions are provided in a 3-page word document along with 2 diagrams and 3 charts.

    $2.49

    ADVERTISEMENT