How do you use the trapezoidal rule to find the integral from 1 to 4 for #6sqrt(lnx)# with n=6?

1 Answer
Steve M
Dec 15, 2016

# int_(1)^(4) 6sqrt(lnx)dx ~~ 15.54800 " "(5dp)#

Explanation:

The values of #y=6sqrt(lnx)# are tabulated as follows (using Excel) working to 5dp

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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_(1)^(4) 6sqrt(lnx)dx ~~ 0.5/2 { 0 + 7.06446 + 2(3.82057 + 4.99533 + 5.74338 + 6.28888 + 6.71561)} #
# " " = 0.25 { 7.06446 + 2( 27.56378 )}#
# " " = 0.25 { 7.06446 + 55.12755 }#
# " " = 0.25 { 62.19201 }#
# " " = 15.54800#

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