Help! 2 unsolved calculus problems!?

Question

hello! i need help with these calculus problems. can anyone please help me find the answer to them??

Use the Midpoint Rule to approximate the integral
5
Evaluate the definite integral.
3

Answer 1

I forget how to solve the first....



2. Find antideriavative

2x^3 + (x^(3/2))/2

Solve by plugging in 5 then subtract that answer from the answer you get when pluggin in 3

Answer 2

I'm going to teach you how to solve something called a "seperable differential equation." You will learn this anyway if you're going to be an engineer or scientist. First, rewrite k√t as k*t^(1/2). OK now basically, multiply both sides by dt to get: dy = k*t^(1/2) dt Integrate both sides (notice that ⌠dy is really ⌠1 dy): ⌠dy = ⌠k*t^(1/2) dt You can pull out the k since it's a constant: ⌠dy = k * ⌠t^(1/2) dt And you know that when you integrate a variable t^n, you get t^(n+1) / (n+1). So this is the final answer ( C is the constant of integration which you only need if you were given an initial condition, like if they told you that y(0)=1 or something) y = k * 2t^(3/2) / 3 + C Voila! Hope this helped you =D

Answer 3

Sorry, wish I could help.