86 Answered Questions for the topic Integrals


What is ʃ e^(1/2)x (dx)?


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


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!


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.


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.. : https://ibb.co/mWAC7x


How do constant c gone inside the log in integrals?

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


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


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


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=


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


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


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


How do you solve this equation

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


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


integral of (x-2)^-3/2

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


Definite Integral with U-Substitution

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 from u(a) to... more


Integration question involving cosh^-1???

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, and... more


Indefinite Integral

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