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90 Answered Questions for the topic Integrals



Integrals Math Calculus


Evaluate the area of a surface of revolution the curve given by a graph of f(x) = x^3 , 1 ≤ x ≤ 2, rotate about the y-axis.

NEED ASAP! Please provide step by step solutions and explanations. Thank you!


Integrals: Inverse Trigonometric

Integrate: dx/[sqrt(8+6x-9x^2)] Please show step by step solution. I have 1/3 arcsin (3x-1) + c as an answer, is that right?
Integrals Math Calculus


the integral of (1/x(sqrt(x^2-4))dx

Need to be answered ASAP. Please show step by steps and explain what was done in each step and why. Thanks so much!
Integrals Calculus Integral


What is ʃ e^(1/2)x (dx)?

Integrals Math Calculus


Let f : [a, b] → R be a differentiable function and let P be a partition of [a, b]. Show that L(P, f′) ≤ f(b) − f(a).

 Let f : [a, b] → R be a differentiable function and let P be a partition of [a, b]. Show that L(P, f′) ≤ f(b) − f(a).   Hint: Use the Mean-Value Theorem.(Recall that, if P = (x0,x1,...,xn), then... more
Integrals Calculus Area


Double integral - calculating area

Calculate the area of the region bounded by the two curves, y = 4 - x2 and y = x + 2.   The answer is meant to be 9/2 but I just cannot get it!!! Maybe my bounds are incorrect.... help!
Integrals Calculus


Need help estimating integrals

Estimate the integral ∫15(top)3(bottom)(−x2+0.07x−0.9)dx using a right Riemann sum with 6 subintervals.
Integrals Calculus Calculus 2


How do I solve this Integral? (Pic attached in link)

I have been stuck on this integral for 3 hours. Here is what I have so far.. :


How do constant c gone inside the log in integrals?

∫dx/(x+1) - ∫dx/(x+2) = log| (x+1)c/(x+2) |
Integrals Math Math Help


This was on my first Calc 2 quiz: $2\int_{-3}^{3}e^x^4dx$

I feel that there should be another x in the problem so that u sub works, or something, as it is I believe it is a partial gamma function or something, but I know we should not learn those until... more
Integrals Math Science


I have a question regarding integrals, which I have not been able to solve

The function to be integrated is the following: f(x)=(√x)/(x2 + ln(1+x))   In addition to this we were asked to confirm if the function converges or not. When plotted it is observed to tend... more
Integrals Geometry


Draw a graph of the signed area represented by the integral and compute it using geometry.

∫10−10|x|dx∫−1010|x|dx =


Calculate the integral below, assuming that ∫50f(x)dx=5∫05f(x)dx=5 and ∫50g(x)dx=12∫05g(x)dx=12. ∫50(6f(x)−13g(x))dx=

Calculate the integral below, assuming that ∫50f(x)dx=5∫05f(x)dx=5 and ∫50g(x)dx=12∫05g(x)dx=12. ∫50(6f(x)−13g(x))dx=
Integrals Math Calculus


What M value should I use? (how do i find it)

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... more
Integrals Summation


Sigma notation with area under a curve, lower and upper rectangles

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 for the... more


Integration of 1/(x^2(2+x^3)^(1/3)) dx

integral cccalculus with respect to dx
Integrals Calculus Derivatives


What is the integral of a function: (e^(-x))cos(x/2) 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 me a definite... more


Net change/word problem/integrals

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 change... more
Integrals Calculus


How do you solve this equation

Find the integral of sec2(x)tan2(x)dx
Integrals Math Calculus


What's wrong with this integral?

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 u = d + L -x. Then du= -dx.... more
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