Problem

Evaluate the integral.
01x1x22x+5dx
01x1x22x+5dx
(Type an integer or decimal rounded to three decimal places as needed.)

Answer

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Answer

The approximate value of the integral 01x1x22x+5dx is 0.112.

Steps

Step 1 :The integral is a definite integral from 0 to 1. The integrand is a rational function.

Step 2 :We can use numerical methods to approximate the value of the integral. One common method is Simpson's rule, which approximates the area under the curve by dividing it into a number of equal-width intervals and approximating the area of each interval with a parabola.

Step 3 :We set n = 1000 and h = 0.001.

Step 4 :We calculate the x values from 0 to 1 with a step of 0.001, and the corresponding y values using the function x1x22x+5.

Step 5 :We then calculate the integral using Simpson's rule and get an approximate value of -0.11157177565710732.

Step 6 :The approximate value of the integral 01x1x22x+5dx is 0.112.

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