263 Answered Questions for the topic integral


Integrals Problem

The marginal cost of manufacturing x yards of a certain fabric is C′(x)=3−0.01x+0.000006x^2 (in dollars per yard). Find the increase in cost if the production level is raised from 1500 to 9500... more


Integrals Problem

A factory produces bicycles at a rate of 95+0.1t^2 −1.1t bicycles per week (t in weeks). How many bicycles were produced from day 15 to 28?


Integrals Problem

The interval [0,4] is partitioned into n equal subintervals, and a number xi is arbitrarily chosen in the i^th subinterval for each i. Then:lim (n→∞) n ∑ i=1 [(2xi+3)/n] = ?


Integrals Problem

Estimate the area under the graph of f(x)=(x^2)+3x from x=5 to x=8 using 3 approximating rectangles and left endpoints.Approximation =


Evaluate the integral (step by step process)

∫x4+X2+4/ x6+4x4+4x2 dx


Integrals Problem

 Consider the function f(x)=(9)/(x^(2))-(7)/(x^(7)) . Let  F(x) be the antiderivative of f(x) with F(1)=0.Then F(x)=


Integrals Problem

Suppose f''(x)= -25sin(5x) and f'(0)=-5 and f(0)=6f(pi/4)=


Frustrating Integral, help

the integral of (x^4 + X^2 + 4) over (x^6 +4x^4 + 4x^2) then dx on the middle of the fractioni got stuck after the partial fraction decomposition


Step by step of evaluating the integral.

Evaluate the integral (x4+X2+4 all over x6+4x4+4x2) dx.Evaluate the integral cosh-1 x dx.Help please!!


Hello, please help me with my intergral

So the equation goes something like this, it is a fractionthe integral of (x^4 + X^2 + 4) over (x^6 +4x^4 + 4x^2) then dx on the middle of the fractionPlease show me how to solve it and provide me... more


Pls slove the math

Find the surface area of the region under the curve (x/a)2/3 + (y/a)2/3 =1 by revolving about x-axis.
Integral Calculus


Find the area enclosed by the given curves

y = 8 cos(𝜋x),    y = 8x2 − 2


Applications of Integration

How would you prove the volume of a cone equation by rotating the line about the x-axis if you have (h,r) and (h,0)? Start by finding the equation of the line.

Calculus, Applications of Integration

How would you find the volume of the solid of revolution formed when the curve 𝑦=(√sin𝑥) between 𝑥=0 and 𝑥=𝜋 is revolved about the 𝑥-axis?
Integral Math


Math Integral grade 11

Please help answer question 3 with steps, much appreciated!3 . A curve is such that dx/dx = 6/x^2 - 5x and the point (3,5.5) lies on the curve. Find the equation of the curve.


Evaluate the integral using the indicated trigonometric substitution.

∫5x^3(sqrt(9−x^2))dx and x =3sin(θ)


I need some help with math

For 0 ≤ t ≤ 12 , a roller coaster car has position (x(t),y(t)) with velocity vector ⟨10, −tsin(πt/4)⟩ , where x(t) and y(t) are measured in meters and t is measured in seconds. At time ... more


*integral sign* (6w *square root* w) dw


Hi, I need help with math

What is the slope of the line tangent to the polar curve r=4θ^2 at the point where θ=pi/4a) pi/2b) pi^2/4c) 8+pi/8-pid) something else?


Please help with math question

A curve is defined by parametric functions x(t) and y(t), where dx/dt = 3t^2 and dy/dt = t^7-2t^4. For what positive value of t is d^2y/dx^2 = 1?a) 1.202b) 1.149c) 1.079d) 1.525
Integral Calculus Derivative


AP CALC AB: Interpretations & Applications of the Derivative & Definite Integral

How would you solve for a) & b) with a calculator?I have a TI-89 Titanium.At time t=0, a tank contains 38 gallons of water. Beginning at t=0, water flows into the tank at a rate of E(t) =... more
Integral Math Calculus Maths


Integral logarithmic calculus math help.

Pls find ∫x(2+x)logx2dx I dont know how to do calculus of a logs base, here x is the base of the log.
Integral Math Calculus


Using her lathe, a woodworker creates a wooden vase that is 15cm tall, with a side profile that can be described with the equation y=5 + 0.1e^0.2x

Using her lathe, a woodworker creates a wooden vase that is 15cm tall, with a side profile that can be described with the equation y=5 + 0.1e^0.2x What is the volume of the vase?Note from... more

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