How do you use the trapezoidal rule with n = 4 to approximate the area bounded by the curves #y = sin2x#, the lines x = 0, y = 0, and x = 1?

1 Answer
Nov 3, 2016

Answer:

# int_0^1sin(2x)dx ~~ 0.693 # (3dp)

Explanation:

The values of y are tabulated as follows (using Excel)

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Using the trapezoidal rule:
# int_a^bydx ~~ h/2{(y_0+y_n)+2(y_1+y_2+...+y_(n-1))}#

we have:
# int_0^1sin(2x)dx ~~ 0.25/2{ (0.00000 + 0.90930 + 2(0.47943 + 0.84147 + 0.99749)} #

# :. int_0^1sin(2x)dx ~~ 0.125{ 0.90930 + 2(2.31839)} #
# :. int_0^1sin(2x)dx ~~ 0.125{ 0.90930 + 4.63678} #
# :. int_0^1sin(2x)dx ~~ 0.125{ 5.54608} #
# :. int_0^1sin(2x)dx ~~ 0.69326 #