The functions f and g are integrable and f(x)dx 2. f(x)dx 4, and g(x)dx= -3. Find the values of the following definite integrals. 2.

Q: Find the Particular Integral for the given differential equatiorn d²y dy +3- dx +6y =2x²+x+5 dx2…

A: using expansion,         (1+x)-1 =1-x+x2 -x3+...

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Q: 1. S(x3/2 + 2x + 1) dx

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Q: The value of the definite integral' f(x )dx for f(x) = 3 is:

A: We are going to evaluate the value of the given definite integral for f(x)=3

Q: 1. Solve the following integral by using the Integration by Parts. (a) x sin x dx (b) e 2x sin 2x dx

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Q: 4. Evaluate the given integral. |(x + 1)(x – 3)| dx -2

A: Solution:Given∫-20(x+1)(x-3)dx =∫-20(x2-2x-3)dx= ∫-20(x2-2x-3)dx= x33-2x22-3x0-2=0--83-4+6=23

Q: 2. Compute the following. When evaluating the definite integral, change the limits of integration.…

A: (a).  The given integral is: ∫x21+x35dx

Q: In the function given. Evaluate the integrals.

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Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

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Q: Use the values f(x) dx = 8 and g(x) dx = 4 to evaluate the definite integral. (a) Зд(x) dx 0. (b)…

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Q: 1. Find the definite integrals of the following functions : (a) L. 4.x dx (h) dx ex +1 -2 0. (b) /…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: evaluate the given integral.

A: Use Substitution method to determine the value of  integral .

Q: Evaluate the given integral 2x +3 -dx- (x + 1) (x – 1)²

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Q: (sec2 x + csc2 x)cos2 x dx

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Q: 2. Evaluate the given integral. |2.x² – æx| dx

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Q: Evaluate the integral. 4 dx (x – 4) (x – 1) | (Use symbolic notation and fractions where needed. Use…

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Q: Q1. Evaluate the following Integrals 1 dx 1- cos x .2 +x - 2x +3 dx

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Q: Q2) Evaluate the integral x dx a -0.

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Q: Q2) Find the integral value for the following functions dx 4. S x2Vx2-1 eCos-1x 5. S V1-x2 6. Se…

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Q: For which of the following integrals would the substitution method be effective? dx x² + 1 æ/1+x² dx…

A: Among the given options, Substitution can be used in both 1 and 2 but in third one the product rule…

Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

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Q: a) Evaluate the following integrals 1) xe3*dx 2) | x2 sin x dx 3) | x sin 2x dx

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Q: For the given integral (x+1) dx V (x+1)2

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Q: 8. Find the value of the constant C for which the integral 11x 11C dx x* + 1 4x + 1 converges. C =…

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Q: 2. Given the integral: S, e'/x dx; n = 8

A: Given,          ∫13e1/xdx;  n=8

Q: Find the value of the following definite integrals. Show your solution. 1. f(x¹+4) dx 2. (cos x +…

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Q: a) Evaluate the following integrals 1)/ xe dx 2) x2 sin x dx 3) x sin 2x dx

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Q: Given: (25(x)dx e-x3 There is a function f (x) such that when u = -x³, the resulting integral is…

A: topic - functions

Q: Evaluate the following indefinite integrals. 1. S(5x + 4)11 dx 2. Sx (x² + 2)17 dx 3. fx²(9 – x³)5…

A: The solution is given below

Q: I. Evaluate the following integrals. 3.x5 dx V2 – x3 1. - 2* + e2" sin(2") dx sin(2") 2. 2x + 3 dx…

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Q: Q1)Evaluate the following integral: 2 1-x dx 1+x2,

A: 1 We have to evaluate the integral ∫021−x1+x22dx. Now,…

Q: If f is continuous from the integral 0 to 9 of f(x) dx = 20. find the integral 0 to 3 of x f(x^2)…

A: Given. ∫09f(x) dx=20 To determine. ∫03xf(x2)dx Let x2=u Differentiate the function x2=u.…

Q: a) S dx =? 2 X*V2x+4

A: Given: ∫dxx22x+4

Q: x = 3. Find the value of k, if ][ƒ(x)-kx]dx=7. Given f(x)dx=-Sand f(x) dx = 3 Using the properties…

A:

Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

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Q: 1 dx x² +1 e +

A: solution:-∫02ex+1x2+1dx=∫02exdx+∫021x2+1dx=ex02+tan-1x02=e2-e0+tan-12-tan-10=e2-1+tan-12     Ans

Q: For p > 0 and a > 0 express the following integral in terms of the gamma function: tP-le-at dt.

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Q: 9. Calculate the following definite integrals by hand. (a) x² + 4x dx (b) cos(x) dx (c) o JE 3 dx

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Q: evaluate the given integral.

A: The given integral ∫2x+1xx2+4dx can be evaluated as, ∫2x+1xx2+4dx=∫2x2+4dx+∫1xx2+4dx The integral…

Q: Q2) Evaluate the integral x* dx 0.

A: To evaluate the given integral

Q: f(x) dx = -3, f(x) dx = 8, and g(x) dx = 8, find the following integrals. If 1. f(x) 2. + 6] dx =

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Q: In the function given. Evaluate the integrals.

A: Given integral: We have to find 3∫14fxdx We know that ∫14fxdx=8 Therefore, 3∫14fxdx=3×83∫14fxdx=24

Q: (d) L™ x³ cos(x* + 5) dx. (e) f(2x – 1)³ dx . -

A: For the given integral  ∫0π4x3cos(x4+π2) dx

Q: Evaluate the definite integral. *2 e 1/x* dx J1 +s

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Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

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Q: Find the value of the constant C for which the integral 5x 5C dx 2 X² + 1 Зх + 1 converges. C = 3…

A: Convergence of integral

Q: Evaluate the given definite integral. -2 . Jx(3-x²)*dx -3 -2 S2x(3-x)°d dx = (Type an integer or a…

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Q: Q1. Evaluate the following integrals. Dfxe" dx (2)f(x +1)e"dx (3)f(2x -3)e-*dx (4

A: As per our guidelines , we can only solve first three sub-parts of a question. Please repost other…

Q: Q3: Find the integral for the following functions: - -6 dx 1) L 2 x+2 2) S 3co t(x). csc²(x) dx 3)…

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Q: Q2/ Find the value of the following integrals: 1- [(* |(x+ y)dx + (y - x)dy), when c is given by, x…

A: The line integral ∫CF1dx+F2dy involves the integration over a specific path. In this problem, we…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.