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Sagot :
The basic theorem of calculus states that the function must be differentiable throughout the specified limit interval. So all options are correct.
In the given question, we have to select every definite integral below that can be evaluated using the fundamental theorem of calculus (there may be more than one).
The given integrals are:
- [tex]\int_{-\pi}^{\pi}sin^7(4x)cos^8(3x)dx[/tex]
- [tex]\int_{-5}^{12}(x\text{In}x+2x-1)dx[/tex]
- [tex]\int_{0}^{4}(12x^{16}-5x^{11}+81x^{8}-208432x^{2}+x-2)dx[/tex]
- [tex]\int_{-1}^{1}\frac{1}{x}dx[/tex]
- [tex]\int_{1}^{9}|x|dx[/tex]
As we know that,
A definite integral is a formal estimate of the area beneath a function. Integrals can reflect a region's (signed) area, the total value of a function that changes over time, or the amount of a given thing given its density.
The basic theorem of calculus states that the function must be differentiable throughout the specified limit interval.
Within the specified limit interval, the integral in the supplied option is differentiable.
Therefore, each choice is valid.
To learn more about fundamental theorem of calculus link is here
brainly.com/question/2293034
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