Integral approximation: int [a, a + delta-a] x^3 dx

[lop]

Suppose I have a definite integral
\(\displaystyle A = \int_{a}^{a+\delta a}x^3dx\)

how could I approximate for small \(\displaystyle \delta a\) given integral just as a rectangle?

 

[pka]

Suppose I have a definite integral
\(\displaystyle A = \int_{a}^{a+\delta a}x^3dx\)
how could I approximate for small \(\displaystyle \delta a\) given integral just as a rectangle?

I have no idea what you mean. But here is the obvious:
\(\displaystyle \displaystyle {\int_a^{a + \delta a} {{x^3}} dx = \left. {\frac{{{x^4}}}{4}} \right|_a^{a + \delta } = {4^{ - 1}}\left[ {{{\left( {a + \delta } \right)}^4} - {{\left( a \right)}^4}} \right] = ?}\)

 

[lop]

I have no idea what you mean. But here is the obvious:
\(\displaystyle \displaystyle {\int_a^{a + \delta a} {{x^3}} dx = \left. {\frac{{{x^4}}}{4}} \right|_a^{a + \delta } = {4^{ - 1}}\left[ {{{\left( {a + \delta } \right)}^4} - {{\left( a \right)}^4}} \right] = ?}\)

What is the approximate value of an integral if the function is (roughly) constant over the integration range?

Reference https://www.physicsforums.com/threads/relate-wavelength-and-energy-scale.885442/



Is it possible to find approximate value of the integral if the function is roughly constant over the integration range. For example using a rectangle method.

What is the approximate value of an integral if the function is (roughly) constant over the integration range?

Reference https://www.physicsforums.com/threads/relate-wavelength-and-energy-scale.885442/

What is the approximate value of an integral if the function is (roughly) constant over the integration range?

Reference https://www.physicsforums.com/threads/relate-wavelength-and-energy-scale.885442/sad

 

[lop]

Is it possible to approximate this integral if the function is roughly constant over the integration rage, for example using rectangle method?