Use symmetry to evaluate the following integrals. \int_{-2}^{2}(x^{2}+x^{3})dx

diferira7c

diferira7c

Answered question

2022-01-03

Use symmetry to evaluate the following integrals.
22(x2+x3)dx

Answer & Explanation

Mason Hall

Mason Hall

Beginner2022-01-04Added 36 answers

Step 1
Given: An integral 22(x2+x3)dx
By symmetry an integral of form aaf(x)dx can be written as a0f(x)dx+0af(x)dx
Therefore, 22(x2+x3)dx can be written as:
22(x2+x3)dx=20(x2+x3)dx+02(x2+x3)dx
Step 2
Now integrating the above function with respect to x.
22(x2+x3)dx=20(x2+x3)dx+02(x2+x3)dx
=[x33+x44]20+[x33+x44]02
=[(0+0)(83+4)]+[(83+4)(0+0)]
=834+83+4
=163
Thus, the value of 22(x2+x3)dx is 163
Lynne Trussell

Lynne Trussell

Beginner2022-01-05Added 32 answers

(x2+x3)dx
Lets
karton

karton

Expert2022-01-11Added 613 answers

Given:
22(x2+x3)dxx2+x3dxx2dx+x3dxx33+x44(x33+x44)|22233+244((2)33+(2)44)Answer:163

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