448 Answered Questions for the topic integral calculus

Integral Calculus Math Calculus Statistics

08/09/21

find the formula for the general term aₙ of the sequence starting at a1
find the formula for the general term aₙ of the sequence starting at a1{-4/25, 5/36, -6/49, 7/64, ...}aₙ =
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Integral Calculus Calculus Probability Integral

08/07/21

probability density function
Let X be the amount of time (years) before a new battery stops working. X has the probability density functionf(t) = { C e^(-0.4t) , t ≥ 00 , otherwise,where C is a constant.Find C (using (Pr(-inf... more
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Integral Calculus Calculus Probability Integral

08/07/21

probability density function, find SD(X), find cumulative distribution function (CDF)
Let X be the amount of time (years) before a new battery stops working. X has the probability density functionf(t) = { C e^(-0.4t) , t ≥ 0 0 , otherwise,where C is a... more
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Integral Calculus Calculus

08/04/21

A region is bounded by x=y^2 and x=4 and y=0 and revolved about the line x=5. Find the volume using the shell method.
Use the shell method to find the volume.
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Integral Calculus Calculus Area

08/04/21

Find the area of the region bounded by y=1/x^2,y-4, and x=5. Use dy to integrate and/or differntiate.
In this question find the area but use dy to set up the integral and bounds.
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Integral Calculus Integral

07/26/21

Evaluate the following integrals
1. ∫ (x−1)(2x3+2x2+3x+2)dx / x3(x+1)2. ∫10dx / 4x3−4x2+5x
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Integral Calculus Integral

07/24/21

Determine the integral
Determine the integral of x y dx dy. Use inner limits=0 to (y + 1) and outer limits=0 to 1.
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07/24/21

find the indefinite integral by using partial fractions

∫x^2+3x-7⁄(2x+3)(x+1)^2dx
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Integral Calculus

07/23/21

VOL CROSS-SECTION DISK WASHER
Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves 𝑦=sqrt(x-1),y=0, x=2,x=4 about the x-axis.
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Integral Calculus

07/23/21

VOL CROSS-SECTION DISK WASHER
Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves 𝑦=1/x,y=0,x=1,x=3 about the x-axis.
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Integral Calculus

07/23/21

VOL CROSS-SECTION DISK WASHER
Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves 𝑦=e^x, y=0,x= −1, and x=2 about the x-axis.
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Integral Calculus

07/23/21

VOL CROSS-SECTION DISK WASHER
Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves 𝑦=x^2,x=4,y=0 about the x-axis.
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Integral Calculus Calculus Series Sigma Notation

07/22/21

Can anyone walk me through this problem?
Apply integration to the expansion 1/1+x = ∑∞n=1 (-1)n xn = 1-x2 - x3 + ... to show that for -1< x< 1, ln (1+x) =∑∞n=1 ((-1)n-1 xn ) / n
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Integral Calculus Calculus

07/22/21

Find the value of the definite integral if you know that...
13.5 8.5 13.5 11 ∫ f(x)dx = 2 ∫ f(x)dx = 8 ∫ f(x)dx = 8 ∫ f(x)dx = -146 6 ... more
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Integral Calculus

07/22/21

ARC LENGTH AND SURFACE AREA
Find the area of the surface obtained by rotating the curve y=1+6x^2 from 𝑥=0 to x=4 about the y-axis. 
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Integral Calculus

07/22/21

ARC LENGTH AND SURFACE AREA
Find the area of the surface obtained by rotating the curve y=cos(2x),0≤x≤(𝜋/6),about the 𝑥x-axis.
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Integral Calculus

07/22/21

ARC LENGTH AND SURFACE AREA
Find the length of the curve defined by y=4x^(3/2)-5 from x=5 and x=7.
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Integral Calculus

07/22/21

THE SHELL METHOD
The region bounded by y=x^2-3x+2 and y=0 is rotated about the y-axis. Find the volume of the resulting solid by any method.
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Integral Calculus Integral

07/19/21

Other Applications of Integration
1. The area bounded by the parabola ay = x2 and the line y = b is revolve about the x − axis. Find the volume generated. (use cylindrical shell method)2. How far from the x-axis and y-axis is the... more
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Integral Calculus Integral

07/19/21

Other Applications of Integration
1. The area bounded by the curve y = e−x, the axes and the line x = 2 is revolved about ox. Find the volume generated. (use circular disk method)2. Find the volume of the torus formed by revolving... more
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Integral Calculus Integral

07/16/21

Application of Integration: Plane Area
Show your mathematical maturity by giving COMPLETE complete solution to each of thefollowing items.1. Determine the area bounded by the curves y = 6x − x2 and y = x2 − 2x.2. Determine the tangent... more
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Integral Calculus Integral

07/16/21

Application of Integration: Plane Area
Show your mathematical maturity by giving COMPLETE complete solution to each of thefollowing items.1. Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.2. Find the area bounded by... more
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Integral Calculus

07/12/21

Definite Integrals
 10 ∫√x √1+x √x dx  π/3π/6 ∫ (1-cos 0) csc2 0 d 0  e1 ∫lnx/x dx
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Integral Calculus

07/12/21

Indefinite Integral
∫(1+sec2 x) / (1 + tan3 x)cos2x dx ∫ cos x / sinx+sin3x dx
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Integral Calculus Integral

07/12/21

Evaluate using Wallis’ Formula.
∫0π/2 sin4y cos7 ydy ∫10 (1-x2) 5/2 dx
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