244 Answered Questions for the topic integral calculus

Integral Calculus

3d

#### Substitution Integral Question

Use the substitutions tan(x/2) = tdx = 2/(1+t2)and evaluate∫1/(3-5sin(x))dx

#### Evaluate the Riemann sum

If f(x) = 4x2 − 5x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints.

Integral Calculus

8d

#### If f is continuous for all c, which of the following integrals necessarily have the same value?

I. ∫ab f(x)dxII. ∫0b-a f(x+a)dxIII. ∫a+cb+c f(x+c)dxA) I and II onlyB) I and III onlyC) II and III onlyD) I, II, and III onlyE) No two necessarily have the same value

Integral Calculus

9d

#### Let f be a continuous function on the closed interval [0,2]. If 2≤ f(x)≤ 4, then the greatest possible value of : ∫(0 to 2) f(x)dx is:

A) 0B) 2C) 4D) 8E) 16

#### What is the value of C so that the following function is a probability density function? f(x)=Cx^9.5 --> see description

f(x)=Cx9.5 if 0≤x≤2, 0 otherwise

#### How do I integrate 1000e^-.0415t - 250te^-.0415tdt?

1000e-.0415t-250te-.0415tdt

#### Honey is poured into a glass jar at a rate of r(t)=4e^(-0.35t) ounces per minute, where t is measured in minutes and 0≤t≤5. If there is 3 ounces of honey in the jar at time t=0, how much honey is in t

Honey is poured into a glass jar at a rate of r(t)=4e-0.35t ounces per minute, where t is measured in minutes and 0≤t≤5. If there is 3 ounces of honey in the jar at time , how much honey is in the...
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#### It can be shown that ∑_(i=1)^n i^3 =(n^2 (n+1)^2)/4. Use this fact along with the limit of Riemann sums (∑_(i=1)^n f(xi

It can be shown that ∑ni=1 i3=(n2 (n+1)2)/4. Use this fact along with the limit of Riemann sums (∑ni=1 f(xi* )∆xi ) using a regular partition of the interval [0,b] (b>0) and the right endpoints...
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Integral Calculus Integral

23d

#### integrate the following question

integrate the following question :∫ (ey - y e-y ) dyPlease write the answer with explanation steps

Integral Calculus Calculus

10/17/20

#### (Arc length and surface area) Rotate the graph of 𝑔(𝑥)=𝑒^(−9𝑥) on the interval [0,7] about the x-axis to generate a surface with x square units.

Integral Calculus Calculus

10/16/20

#### (Arc Length and Surface Area) Compute the surface area of revolution of 𝑦=(4−𝑥^(2/3))^(3/2) about the x-axis over the interval [3,8].

Integral Calculus Calculus

10/09/20

#### Find the volume of the solid obtained by rotating the region enclosed by the curves y = 15-x, y = 3x+11 and x = -1 about the x-axis.

Integral Calculus Calculus

10/09/20

#### Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=18−x, y=3x−6 and x=0 about the y-axis.

Integral Calculus Calculus

10/09/20

#### Find the volume of the solid obtained by rotating the region enclosed by the curves x = 1, x = 6, y = (1^4−x^4), y = 0 about the y- axis.

Integral Calculus

10/06/20

#### calculate the double integral (x^2+y^2)dxdy in the circle x^2+y^2=2x

convert it to polar rdrd0. and then solve. the circle is at (1,0) not the origin.

Integral Calculus

10/01/20

#### Using Greens Theorem

Use Greens theorem to evaluate ∫ F • dr along the given positively oriented curve C where:C F= (xy − 4 ye2x )i + ( y2 − 2e2x )j and C is the boundary of the region in the first...
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Integral Calculus Math

09/29/20

#### Evaluating triple integrals

Consider2 √ (4-z2) 2 ∫ ∫ ∫ xz dxdydz0 0 √(y2+z2)the question is to evaluate the integral by firstly converting to cylindrical coordsand to sketch the integration...
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#### Calculus 2 MacLaurin Series

Let F(x) = ∫ (from 0 to x) e-3t^4 dtFind the MacLaurin polynomial of degree 5 for F(x).

#### Calculus 2 Series

Find the sum of the series ∞ ∑ (-1)n [(x15n)÷(n!)]n=0It will be a function of the variable x

Integral Calculus

09/21/20

#### Surface Integral

Evaluate the surface integral ∫ ∫ yzdS , s where S is the part of the half-cylinder x2 + y2 = 9, y ≥ 0 , that lies between the planes z = 0, and x + z = 5 .

Integral Calculus Probability

09/19/20

#### PLEASE CAN ANYONE SLOVE 1(A) ONLY. THANK YOU

Probability theory tells us that if the average time between events is k, the probability that x, the time between events, is between a and b is given by,P(a ≤ x ≤ b) = ∫ ba f(x) dx ------ equation...
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#### Triple integral by converting to cylindrical coords.

Consider 2 √ (4-z2) 2 ∫ ∫ ∫ xz dxdydz0 0. √(y2+x2)the question is to evaluate the integral by firstly converting to cylindrical coordsand to sketch the...
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09/17/20

#### Evaluate the line integral with respect to arc length.3 variables

Evaluate the line integral with respect to arc length where C is given by ∫c x ds x = t, y = t sin t, z = t cos t, 0 ≤ t ≤ √(2)firstly subbed t into equation as x=tthen differentiated x, y and...
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Integral Calculus Probability

09/16/20

#### Please can anyone solve 1(a) and 1(b). I need help. Thank you in advance.

Probability theory tells us that if the average time between events is k, the probability that x, the time between events, is between a and b is given by,P(a ≤ x ≤ b) = ∫ ba f(x) dx ------ equation...
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#### Find the rate of revenue change with respect to time.

isMobile phone manufacture will be releasing a new version of their smart phone model. Theydetermined that t months after the new phone introduced to the market;The manufacturing facility can...
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