I was asked to calculate the area between two functions, y=e^x and y=x using midpoint riemann sums from 0-2 with n=4. so i found my answer by subtracting the second sum from the first. The second...

I was asked to calculate the area between two functions, y=e^x and y=x using midpoint riemann sums from 0-2 with n=4. so i found my answer by subtracting the second sum from the first. The second...

I got the answer to this problem from my teacher but I don't understand why that's the answer: y=√1+x^3 , domain 1≤x≤2 and with 50 intervals therefore width is 1/50. The Sigma notation...

integral cccalculus with respect to dx

The answer which I got was (e^(-x))sin(x/2)-cos(x/2)(e^(-x)) However all the math solvers on the internet are giving different answers. Could you clear things up and tell...

Water flows into a reservoir at a rate of 1500 + 7t2 gallons per hour. since there is a tiny hole in the reservoir, the water leaks out at a rate of 4t + t2 gallons per hour. What is the net...

Find the integral of sec2(x)tan2(x)dx

I'm trying to integrate (x)/(d+L-x) respect to x but I get -(d+L)ln(d+L-x) + d + L -x. The correct answer is -(d+L)ln(d+L-x) -x. What I did was to change the variable...

integral of quantity x-2 raised to three halves need help asap thanks

I have an integral with ∫ (b=0, a=-1) and the inside function is (2t)/[(3+t2)3]dt. The directions tell me to "Evaluate the definite integral by making a u-substitution and integrating...

Evaluate the integral (1/sqrt(x^2 - 5))dx on limits of 3 to 4, using the formula: integral of (1/sqrt(x^2 - a^2))dx. Recall that this formula was found by using the substitution x = a cosh t,...

Can someone help me solve for this indefinite integral?: (u^2 + u)/(2u^3 + 3u^2 + 1)^(2/3) Thank you!

I need help solving a couple of indefinite integrals. It seems all of my homework problems have done the less complicated ones so I'm not sure how to due these ones: First problem: (integral...

I need help solving a couple of indefinite/definite integrals. It seems all of my homework problems have done the less complicated ones so I'm not sure how to do these ones: First problem:...

Find the total area between y=x+14 and y=4x+3 between x = 0 and x =2.

A forest fire covers 2010 acres at time t=0. The fire is growing at a rate of 8√t acres per hour, where t is in hours. How many acres are covered 24 hours later? Round your answer to the...

Evaluate the integral below. ∫_0^1¦∫_y^(2−y)¦ ∫_0^(2−x−y)¦ xy dz dx dy

What is the definite ∫((x2-3x+2)/(x+1)) ? I tried dividing this but I didn't know what to do with the remainder.

The curve is x^3-6x^2+11x-6. I have to prove that the two regions enclosed between the x-axis and the curve are equal. Given is, that the curve cuts the x-axis at x=1,x=2 and x=3. I tried finding...

1. Evaluate the integral S-12 f(x)dx, when f(x)=3-x3 when x is less than or equal to 1; f(x)=x2 when x is greater than one. 2. Evaluate the integrals using the FTC 1. (a)...

this is a calculus prblem on anti derivatives and integrals. please help.