448 Answered Questions for the topic integral calculus

Integral Calculus Calculus

02/18/17

Find the lateral surface generated by rotating y=1-x^2 for [0,1] about x-axis and then about y-axis
I'm having a lot of trouble with the set up and integration. Please help me with this problem, thank you. I know you are supposed to use the formula integral(2pi * y * sqrt(1+(y')^2)).
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Integral Calculus Math Help

02/16/17

How to do this integral
∫ (1)/(sqrt(52x -1))dx    Please show me steps. Im having a hard time figuring this out
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Integral Calculus Definite Integration

12/06/16

Find the interval [a,b] for which the value of the following integral is a maximum and explain the reasoning
∫ba (2+x-x2)dx
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Integral Calculus Definite Integration

12/06/16

If f' is continuous on [a,b], show that
2∫ab f(x)f'(x)dx=[f(b)]2-[f(a)]2
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Integral Calculus

12/05/16

Find the interval [a,b] for which the value of the integral ...
∫a b (2+x-x2)dx is a maximum. Please explain your reasoning.
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Integral Calculus Limits

12/05/16

Evaluate the following:
  lim     1      1       2       3             n            — [ (—)9+(—)9+(—)9+...+(—)9 ] n->∞   n      n       n       n             n
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Integral Calculus

12/05/16

If f is continuous on [0,1], prove that
∫01 f(x)dx = ∫01 f(1-x)dx
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Integral Calculus Graphing Shading Calculus 2

09/22/16

Calculus 2 Help Finding the Area of the Curve
1.) Sketch the region enclosed by the curves below.2.) Decide whether to integrate with respect to x or y.3.) Find the area of the region.   2y=5sqrt(x), y=3, and 2y+1x=6
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Integral Calculus Calculus

07/04/16

The integral of 3xsec^2(x) dx
I'm not sure how to start this one. All I know is sec^2 is (1/cosx)^2 is this right?
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Integral Calculus Integration

04/30/16

Finding the integral
Let F(x) = ∫eu^2 + cos(u) du   with upper limit = 7x, lowerlimit = 0 Compute F'(0)   I have no idea how to approach this question the 7x in the upper limit is quite off putting
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Integral Calculus Math Calculus Math Help

04/28/16

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
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Integral Calculus

04/27/16

can =1/10 be factored out of integral dx/(50-10x)
∫dx/(50-10x)=-1/10ln[50-10x]+c   Why does factoring 1/10 a constant out of integral not work.   ∫dx/(50-10x)=1/10∫dx/(5-x) u=5-x du=-1   -1/10ln[5-x]+c
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Integral Calculus

04/27/16

what is the integral of 1dx/(50-10x) is it -1/10ln(50-10x) +c or -1/10ln(5-x) +c
∫dx/(50-10x)=?   Does factoring out 1/10 change the answer.
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Integral Calculus Integration Definite Integration

04/23/16

integration
show that ∫dx/(2+3sinx) [upper limit pi/2, lower limit 0] = ∫dt/((t+ 3/2)2 - (√5/2)2) [ upper limit 1, lower limit 0]     I know that sin(x) = 2t/(t2+1), where t = tan(x/2) but i cannot get the... more
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Integral Calculus Calculus Integrals Integration

04/21/16

Indefinite/Definite Integrals
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:... more
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Integral Calculus Calculus Integrals Antiderivative

04/21/16

Indefinite Integral
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... more
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Integral Calculus Calculus Integrals Calculus 3

03/13/16

Evaluate the integral below.
Evaluate the integral below.   ∫_0^1¦∫_y^(2−y)¦ ∫_0^(2−x−y)¦ xy dz dx dy    
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Integral Calculus Calculus Integral Calculus 3

03/13/16

Find the integral below.
Find the integral below.       ∫∫1_R^ (x+2y) dar={(x, y):0≤x≤3, 1≤y≤4}    
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Integral Calculus Math Calculus

02/17/16

12. The base of a solid is a circular disk with radius of 6. Find the volume of the solid...
12. The base of a solid is a circular disk with radius of 6. Find the volume of the solid if parallel cross sections perpendicular to the x-axis are squares. Set-up but do not evaluate the... more
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Integral Calculus Math Calculus

02/17/16

A bag of sand originally weighing 100 lb was lifted at a constant rate. As it rose, sand also leaked out at a constant rate.
A bag of sand originally weighing 100 lb was lifted at a constant rate. As it rose, sand also leaked out at a constant rate. The sand was half gone by the time the bag had been lifted to 10 ft. How... more
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Integral Calculus Calculus Physics

02/08/16

A vertical right circular cylindrical tank measures 30 ft high and 20 ft in diameter.
A vertical right circular cylindrical tank measures 30 ft high and 20 ft in diameter. It is full of kerosene weighing 51.2 lb/ft^3. How much work does it take to pump the kerosene to the level 4 ft... more
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Integral Calculus Calculus Physics

02/08/16

A bag of sand weighing 144 lbs was lifted at a constant rate to a height of 25 ft
A bag of sand weighing 144 lbs was lifted at a constant rate to a height of 25 ft. How much work was done by lifting the bag this far if the rope weighs 2 lbs per foot?
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Integral Calculus Integrals Areas Area Under A Curve

12/01/15

Find area under the curve
Find the area under the curve h(x)=(3x-2)^3 from x=1 to x=2
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Integral Calculus Math

11/14/15

A high-speed bullet train accelerates and decelerates at the rate of 4ft/s2. Its maximum cruising speed is 90 mi/h.
A high-speed bullet train accelerates and decelerates at the rate of 4ft/s2. Its maximum cruising speed is 90 mi/h.   (a) What is the maximum distance the train can travel if it accelerates from... more
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Integral Calculus Math

11/14/15

A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the brakes. What constant deceleration is required to stop the car in ti
A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the brakes. What constant deceleration is required to stop the car in time to avoid a pileup?     ANSWER:... more
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