Consider the definite integral. (8x- – 1) e*x²-x dx Let u = 4x2 - x. Use the substitution method to rewrite the function in the integrand, (8x – 1) e4x-x, in terms of u. integrand in terms of u:

Q: 2x e dx +1 2x

A:

Q: Calculate the integral in terms of the inverse hyperbolic functions.

A: To make the answer in inverse hyperbolic form, do the following substitutions. Substitute x=sint in…

Q: cos xdx x

A: The given integral is,∫xcosx dx. ∫xcosx dx=x∫cosx dx-∫ddx(x)cosx dx∫xcosx dx=xsinx-∫ddx(x)cosx…

Q: compute the definite integral.

A: ∫1elnx dxx2

Q: 8 cos" 2πt dt

A:

Q: Obtain a formula that expresses the integral ∫cosn x dx

A:

Q: (a) Define a substitution variable u and write / x(x +1)*dx in terms of u. Do not solve the…

A: detailed solution is given below

Q: Compute this integral ∫( sqrt((e^x) +1) dx

A: To Compute this integral ∫( sqrt((e^x) +1) dx

Q: Use the substitution t = tan(x/2) to transform the integrand into a rational function of t and then…

A: Let  I = ∫0π2 5 sin 2x 2 + cos x   dx

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫e3x + 1 dx

A:

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫√(2x + 1…

A:

Q: Find the indefinite integral by making the substitution x = 9 sin e. 6. V81-x2 1 3/2 +C 81 V81-…

A: Option b is correct

Q: Evaluate the definite integral: 4 dx 0 x2+16

A:

Q: Calculate the integral in terms of the inverse hyperbolic functions.

A: Calculate the integral in terms of the inverse hyperbolic functions.

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫ cos (2x +…

A: ∫cos2x+5 dx Now put 2x+5=u Differentiating with respect to x, we get 21+0=dudx⇒2 dx=du⇒dx=du2

Q: Find the Fourier integral of the function when x 0

A:

Q: Ssin( /3x)cos(-2r)dx

A:

Q: 4 dx = x² + 1

A: Given that, ∫-114x2+1dx=4[tan-1x]-11 =4[tan-11-tan-1-1]=4[π4-(-π4)]=4[π4+π4]=4×π2=2π

Q: Evaluate the integral of sin^6 x dx from 0 to T/2.

A:

Q: Evaluate the integral f e² In (x²+1)dx

A: ∫e2ln(x2+1)dx

Q: evaluate the definite integral.

A: Here given Use the standard result of integration as

Q: compute the definite integral.

A: To find: The value of the definite integral ∫01xe-xdx. Concept used: Integration by parts:…

Q: Evaluate the indefinite integral.   ∫ Sec3t  tan 3 t dt

A:

Q: – dx x Inx x²+1

A:

Q: Calculate the integral in terms of the inverse hyperbolic functions.

A: To Calculate the integral in terms of the inverse hyperbolic functions. Given the integral…

Q: 2x (x+2)-5 dx z

A:

Q: Evaluate the integral dx (2a + 6) by making the appropriate substitution: u = dx (2a+ 6)°

A: I have use the substitution

Q: Find the general indefinite integrals of: 1. f cos ntcos(sin(nt)) dt

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

A:

Q: evaluate the integral (Usec. af nitegratun) for the constant बदेशव 1ehan) 5x cos (8x) dx

A: Given

Q: dx 1. -1 V1 – 2x – x²

A: Explained below

Q: (5x° + 4x + Ix Consider the indefinite integral dx x2 – 1 Then the integrand decomposes into the…

A:

Q: Evaluate the integral.  integral cos  - 6  x  dx

A: To evaluate the integral, ∫cos-6xdx Solution: The given integral can be written as,…

Q: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

A:

Q: Find the Fourier integral of the function f(x)= e* when x> 0 and f(-x) = f(x) for k > 0 cosix and…

A: Fourier integral, for even function

Q: (1) [ Evaluate the indefinite integral by substitution: a+bx² dx 3ax+bx3 (2) / sec³xtanxdx T

A:

Q: Evaluate the following integral using the Fundamental Theorem. x-1 dx

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1-X let dx , write the integral by using Beta function

A: Given: ∫011-xxdx

Q: Q1: Evaluate the folowing integrals by using a substitution to reduce it to जकंन standard form: (i)…

A:

Q: Evaluate the indefinite integral. V6 + x°dx + C

A: Evaluate ∫x56+x6dx

Q: Use the Fundamental Theorem to evaluate the definite integral exactly. c2 1 dx 1

A: NOTE: Refresh your page if you can't see any equations. .

Q: Evaluate the integral / 'cos(æ – In x) dx dy.

A: We need to change the order of double integral

Q: Compute the definite integral 2 dx Vx² + 4

A: First, we need to compute ∫xx2+4dx

Q: Obtain a "reduction" formula that expresses the integral cos" x dx in terms of an integral of a…

A: Integration by parts: If u is first function and v is second function then: ∫u(x) v(x) dx=u(x)∫v(x)…

Q: Evaluate the definite integral. 1 dx V2-x

A:

Q: Evaluate the indefinite integrals by using the given substitutions to reduce the integrals to…

A: SOLUTION-

Q: 3 aluate the indefinite integral by using the substitution u = x + x° to reduce integral to standard…

A: Please refer to the image below

Q: In the indefinite integral J 3x²e* dx, the integrand is A 3r © 3x2 D x³+C B.

A: The given integral,    ∫3x2ex3dx

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.