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I am new to the world of calculus and the first thing that I learned is how to calculate the area under the range of a polynomial function, like:
$$\int_1^3 x^2 \,dx$$
when I take the intergal of ##x^2##, I get ##\frac{x^3}{3}##due to the power rule,
but it doesn’t make sense to me,why would you need to divide the coefficient by the exponent and add the exponent by 1?Is there a simple explanation to why such rules exist?
ps:I may use some wrong terms,sorry for that.
$$\int_1^3 x^2 \,dx$$
when I take the intergal of ##x^2##, I get ##\frac{x^3}{3}##due to the power rule,
but it doesn’t make sense to me,why would you need to divide the coefficient by the exponent and add the exponent by 1?Is there a simple explanation to why such rules exist?
ps:I may use some wrong terms,sorry for that.
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