 # Find formulas for the functions represented by the integrals. \int_{1}^{x^{2}}t dt Irrerbthist6n 2021-12-14 Answered
Find formulas for the functions represented by the integrals.
${\int }_{1}^{{x}^{2}}tdt$
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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:
${\int }_{1}^{{x}^{2}}tdt$
$=\frac{{t}^{2}}{2}{\mid }_{1}^{{x}^{2}}$
$=\frac{1}{2}\left({\left({x}^{2}\right)}^{2}-{1}^{2}\right)$
$=\frac{1}{2}\left({x}^{4}-1\right)$
Hence, the function represented by the given integral is $\frac{1}{2}\left({x}^{4}-1\right)$
Step 4:Conclusion
Hence, the function represented by the given integral is $\frac{1}{2}\left({x}^{4}-1\right)$
###### Not exactly what you’re looking for? Shannon Hodgkinson
${\int }_{1}^{{x}^{2}}tdt$
Evaluate the indefinite integral
$\int tdt$
Evaluate the integral
$\frac{{t}^{2}}{2}$
Return the limits
$\frac{{t}^{2}}{2}{\mid }_{1}^{{x}^{2}}$
Calculate the expression
$\frac{{\left({x}^{2}\right)}^{2}}{2}-\frac{{1}^{2}}{2}$
Simplify
Solution
$\frac{{x}^{4}-1}{2}$
###### Not exactly what you’re looking for? nick1337

It is required to calculate:
$\int tdt$
Integral of a power function:

$=\frac{{t}^{2}}{2}$
Problem solved:
$\int tdt$
$=\frac{{t}^{2}}{2}+C$