90 Answered Questions for the topic Integrals

#### 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!

04/13/20

#### 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?

#### 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!

#### 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...
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#### 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!

06/30/18

#### Find the absolute value of the resulting error if the value of the integral from 0 to 3 of x cubed, dx is estimated with 3 inscribed rectangles of equal width.

a) 87.75
b) 15.75
c) 11.25
d) 6.75

Integrals Calculus

04/01/18

#### 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.

03/14/18

#### 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

02/12/18

#### 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...
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#### 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...
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Integrals Geometry

11/19/17

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

∫10−10|x|dx∫−1010|x|dx =

Integrals

11/19/17

#### 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...
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Integrals Summation

05/26/17

#### 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...
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05/12/17

#### 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...
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05/09/17

#### 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...
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#### 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....
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