447 Answered Questions for the topic integral calculus

06/05/22

#### Is it True or False??

The integral of (2x+1)dx from 3 to 4 is equal to (4²+4)-(3²+3).a. Trueb. False

Integral Calculus

06/03/22

#### The slope of the tangent line at any point (x, y) on a curve is 3 √𝑥. If the point (9, 4) is on the curve, find an equation of the curve.

06/01/22

#### Calculus Homework Help

Determine whether the integral is convergent or divergent.
∞
e−1/x / x2 dx
3
If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)

#### The extension, y, of a material with an applied force, F, is given by y = e^(F x 1 x 10^(-3))(e is to the power of F x 1 x 10; 10 is to the power of -3 in that equation)

a)Calculate the work done if the force increases from 100N to 500N using:i) An analytical integration techniqueii) A numerical integration technique[Note: the work done is given by the area under...
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#### Help! Evaluate the indefinite integrals using Substitution. (use 𝐶 for the constant of integration.)

∫(6-12x)(3x-3x2+3)6 dx= ?I'm stuck on this

05/04/22

#### intergral test for convergence of the series

Use the integral test to establish the convergence of the series which is the sum from n=1 to infinity of the terms an=e-n

#### Mathematics Help

The birth rate of a population is b(t) = 2400e0.021t people per year and the death rate is d(t)= 1490e0.015t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer...
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#### Help please: Find the volume of the solid obtained by rotating the region bounded by the curves

Find the volume of the solid obtained by rotating the region bounded by the curves: y=x4, y=1 about the line y=3

Integral Calculus

04/23/22

#### Find the double integral of : -

Find the double Integral of ((x-y)^2)/(x^2+y^2)

#### Help! Evaluate the indefinite integrals using Substitution. (use 𝐶 for the constant of integration.)

Please help I am stumped with this problem.∫(28x+10)(7x2+5x+3)5 dx = ???

Integral Calculus

04/22/22

#### Integral Calculus

Find the area of the region bounded by the parabola y = x^2, the tangent line to the parabola at the point (2,4) and the x-axis

04/19/22

#### calculus integral question

Consider the integral:21∫ x^3 dx3-Use all three methods to approximate this integral with n = 3-Find the exact value of this integral

#### Evaluating integral help

Evaluate the integral.
4
f(x) dx
−4
where f(x) =
2
if
−4 ≤ x ≤ 0
4 − x2
if
0 < x ≤ 4

#### Riemann's Sum and Integrals Question

The value of the limit is equal to the area below the graph of a function f(x) on an interval [A,B]. Find f, A, and B. (Do not evaluate the limit). lim n --> ∞ ∑ni=1 (π)/(6n)tan[(iπ)/(18n)]I...
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#### How do I find the area bounded by a function?

Find the area bounded by f(x)=10-4x2 and the x-axis on the interval [1,2] by finding the limit of the upper and lower sums. Find the width Δx=(b-a)/n, the lower heights f(a+(b-a)(i-1)/n) the lower...
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Integral Calculus Calculus

03/26/22

#### Calculus integration problem

Use implicit differention:
find dy/dx if x^2 - 16xy +y^2 = 1
find dy/dx if cosy - sinx = siny - cosx
find dy/dx if xsiny + ysinx = pi/2√2 at [pi/4, pi/4]
find d^2y/dx^2 if x^2 + 4y^2 = 1

Integral Calculus Calculus

03/26/22

#### improper integral

Why is the integral from x=1 to x=3 of f(x)= 1/(x-2)2/3 improper?

Integral Calculus Calculus

03/23/22

#### Perform Riemann Sum formula for approximating the value of the area of the given equation: y=√x -2 . from x=1 to x= 10

Integral Calculus Differential Equations

03/16/22

#### points (1,4) and (2,12) lie on a curve whose gradient is giiven by dy/dx=6x2-6x+k a)find the value of k b)the equation of the curve

Integral Calculus Math

03/14/22

#### Solving for range with Arc Length Integral

I encountered an interesting problem beyond my skill level, which is thisSOLVE FOR bL = ∫ab √(1+(2wx)2) dxIn which I need to solve for b, but I don't know how to do that yet.If anyone can help I'd...
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#### Use two terms of a Maclaurin series to estimate this integral, and predict your error using the Alternating Series Estimation Theorem.

∫ x^2 * sin(x^2) dxUse two terms of a Maclaurin series to estimate this integral, and predict your error using the Alternating Series Estimation Theorem.Please include formulas so I can follow...
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#### Why doesn't substitution or integration by parts work for this integral?

Why doesn't integration by parts or u-substitution work for this integral?∫ x^2 * sin(x^2) dx

Integral Calculus Maths

03/05/22

#### Newton's law of cooling proposes that the rate of change of temperature is proportional to the temperature difference to the ambient (room) temperature.

(continuation of title) This can be modelled using the equation dT/dt=-k(T-T_a). This can also be written as dT/T-T_a=-k dt.WhereT=Temperature of materialT_a=Ambient (room) temperaturek =A cooling...
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Integral Calculus Math

02/21/22

#### Integrating exponential function beside e^x

I am doing a math assignement where I find the area of a country using functions. I used an exponential equation that was not a base of e. I was able to integrate it using a calculator, but I...
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