Irrerbthist6n
2021-12-14
Answered

Find formulas for the functions represented by the integrals.

${\int}_{1}^{{x}^{2}}tdt$

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Ronnie Schechter

Answered 2021-12-15
Author has **27** answers

Step 1: To determine

Find formula for the function represented by the given integral:

${\int}_{1}^{{x}^{2}}tdt$

Step 2:Formula used

$\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C$ where C is the constant of integration

Step 3:Solution

Consider the given integral:

${\int}_{1}^{{x}^{2}}tdt$

$=\frac{{t}^{2}}{2}{\mid}_{1}^{{x}^{2}}$

$=\frac{1}{2}({\left({x}^{2}\right)}^{2}-{1}^{2})$

$=\frac{1}{2}({x}^{4}-1)$

Hence, the function represented by the given integral is$\frac{1}{2}({x}^{4}-1)$

Step 4:Conclusion

Hence, the function represented by the given integral is$\frac{1}{2}({x}^{4}-1)$

Find formula for the function represented by the given integral:

Step 2:Formula used

Step 3:Solution

Consider the given integral:

Hence, the function represented by the given integral is

Step 4:Conclusion

Hence, the function represented by the given integral is

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Author has **34** answers

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