There is a 2x on the bottom and x^2 on top of the integral symbol
Please help me my teacher did not teach us this:(

Step-by-step explanation:

We can use Part I of the Fundamental Theorem of Calculus:

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

For the first term, replace with , and apply the chain rule to the function. Do the same for the second term; replace

Simplify the expression by distributing and inside their respective parentheses.

Rearrange the terms to be in order from the highest degree to the lowest degree.

This is the derivative of the given integral, and thus the solution to the problem.

answer: 43/157

this is the answer and if you try to prove me wrong your a meanie

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry