Obtain the following integral: as a function of æ, to within an additive constant (do not put a "+c" in your answer). Enter the answer as a function of æ: I

Q: Evaluate the following definite integral, 2 x(2-x)99dx = %3D

A: Given query is to find the value of the integral.

Q: Evaluate the following integral. So e (e +3) da

A: Here I am attaching image so that you understand each and every step.

Q: Evaluate each of the following iterated integrals. а.

A: Integrate it.

Q: Find the integral value for the following functions

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Q: If f(x)is the slope of a trail at a distance of x miles from the start of the trail, what does the…

A: Given∫35f(x)dxAnd we know that the total change theorem :∫35f(x)dx=F(5) - F(3)  ---{1}

Q: Evaluate the given indefinite integral. Indicate u, n, and du. xdx хах 3-x

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Q: teve dt

A:

Q: 32 6. f³² x oriz Steuleve

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: (r+3) dr 3. V7-6r - r

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: following

A: We will find the value of the integral

Q: x' J4-x dx

A: Here we use the substitution 4-x=u to solve this integration.

Q: Find a formula for the function represented by the integral 3t dt

A: Please refer to the image below.

Q: 4. dx +

A:

Q: Evaluate the definite integral. Si f (x) dæ, f (x) =4"-(7a+ 13)/a?

A:

Q: Compute the following integral. Simplify the answer to a single value in lowest terms. 1 S (x^2) /…

A: Given information:  The integral is  ∫01x23x3+1dx. Concept Used: The power rule of integration is…

Q: (a) J ₩을dr

A:

Q: Compute the indefinite integral of the following function. r(t) = (* - 9t,2t – 1,14) Select the…

A: Option A is correct..

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the following definite integrals, a. t(1-t)2 dt = V312 dr b. VI- C. 12x-1|dx=

A: Note: As per our guidelines we are supposed to answer only 3 sub-parts. kindly repost the other…

Q: Express each of the following integrals as a r function. By computer, evaluate numerically both the…

A: Gamma function: The gamma(Γ) function is defined as, Γp = ∫0∞xp-1e-x dx. Properties of gamma…

Q: e

A: Let I be the given integral. I=∫0∞e-x2 dx Let t=x2. Differentiate both sides: dt=2xdxdx=dt2x Since…

Q: Evaluate the following indefinite integral. da I In(x) Note: Don't forget your C! And be sure to use…

A:

Q: If f(x) = /8 +r² dt , find f'(1).

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Q: 53. In x dx

A: Solve the following integral

Q: sen( ds

A: We will find out the required value.

Q: Find integral of the following functions

A: Using gamma integral,

Q: Find the following integral:

A: Given,

Q: Evaluate the following integral or state that it diverges. 1 3 (x- 3)2

A: Given Take antidervative for the given integral using u-substitution

Q: In da for the integral to be equal to What should a be in

A: This is calculus problem

Q: x n x dC

A: Integration by parts : THe formula for integration by parts is given by where u and v are…

Q: Evaluate the following definite integrals, t(1 -t)² dt = а.

A: Solution: ∫-11t(1-t)2dt Expand=∫-11t-2t2+t3dt

Q: Evaluate the given indefinite integral. Indicate u, n, and du. xdx 3-x

A:

Q: Evaluate the definite integral. da r(1+ In z)

A: We will use fact that  ln(a)b=b.ln(a). And ln(1)=0.

Q: Express each of the following integrals as a r function. 8. 9. e- dx Hint: Put x* = u.

A: 8 Given integral is ∫0∞x23e−xdx. The Gamma function is define as follows n=∫0∞xn−1e−xdx Now,…

Q: B. Get the integral of the given function

A:

Q: xdx (x +1Xx+ 2)

A:

Q: Express each of the following integrals as a r function. By computer, evaluate numerically both the…

A:

Q: Compute the indefinite integral of the following function. r(t) = (t° – 5t,8t – 1,10) Select the…

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Q: In the notation for definite integral, | f(x)dæ, a

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Q: - csc? Bdß J cot B+4cot B

A: The value of the given indefinite integral is (1/4)ln(|cot x|) - (1/8)ln(|cot²x + 4|) + C

Q: Evaluate the definite integral (et, et,1) dt

A:

Q: Suppose F(x) = 19 dt. Find a formula for the function F(x4) expressed using an integral. e F(a*) = /

A: The given integral is F(x)=∫19xe-t2 dt

Q: Find the integral for the following functions: - 1) SG+Dax

A: To find the integration [(1/x²)+(1/x)]dx

Q: x² +1 1. х* — 5х+6

A:

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A: ∫ex-14×1x-14dx Let us take u= x-14, then differentiating u with respect to x, we get   du = 12x-14dx…

Q: Write an equivalent integrals for the function f(x,y)=D4x+y for the following base (2,4) y= 2x y

A: Let us considre the function z=f(x,y) the integral under the region R  xy-plane is obtained as…

Q: Evaluate the following integral by using the substitution method sinvw dw M.

A: ∫sinwwdw We need to Solve the above integral by substitution

Q: Evaluate the following integrals C. [x√x + 1dx

A: