1 -dx х6—х

Q: Use the Table of Integrals to evaluate the integral

A: To determine: The value of the given integral

Q: rp= dx bo 1. to

A:

Q: Use the Method of Substitution to find the indefinite integrals: a) / te“dt (q

A:

Q: Evaluate the integral, if it exists.    ∫0T (x4 - 8x  +7) dx

A:

Q: 2. Use a substitution to change the integral into one found in the table of integrals, then…

A:

Q: Use the appropriate substitution to evaluate the following integrals: - dx 9x² + 1

A: The given integral is: I=∫x9x2+1dx

Q: Use Romberg integration to find an 0(h*) approximation for the following integral =| In(x² + 2)dx

A: Given, I=∫01lnx2+2dx. Using Romberg integration, Suppose,  h=b-an, n=1 Therefore, h=1…

Q: Evaluate the integral

A: To integrate,

Q: Evaluate the integrals

A:

Q: Rewrite the integral using substitution: 3 ₁³ (x² cos(4x³)) dx

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. 2x V…

A:

Q: Evaluate the integral by making the given substitution. x-Vx3 + 10 dx, u = x3 + 10

A:

Q: x3 sin(x) dx

A: Solve by integration by parts

Q: Use the Table of Integrals to evaluate the integral. e70 sin 60 de

A:

Q: Use any method to evaluate the integral. 8 dx (16x? + 1)?

A:

Q: sin y – ex y' cosy

A:

Q: Evaluate the integral, if it exists.

A: Given: I=∫04x-1dx for evaluate given integral, we break it in two parts as given below…

Q: Evaluate the integral using the given substitution. (Vx cos (x3/2- 4) dx

A:

Q: Efxe*dx (1+x)2

A:

Q: Use a Table of Integrals to evaluate the integral. 2ædx xª + 9

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration. -6x…

A: We have to evaluate ∫e-6xdx ,   by substituting u=-6xWe have to evaluate ∫dt1-7t6 ,   by…

Q: Evaluate the integral. 1 x + dx J4

A:

Q: sin (x²) + C

A:

Q: cos(x* + 2) dx

A: To Evaluate: ∫x3cosx4+2dx Concept: ∫cosxdx=sinx+C

Q: Use a table of integrals to evaluate the definite integral.

A: Let the given integral be y - y = ∫012x3ex2dxy = ∫01x2ex22xdxLet,t = x2Differentiating on both sides…

Q: XV3x2 – 2 dx 1

A:

Q: Find the integral by algebraic substitution: ∫dx/√1+4x

A: In some cases integrals can be simplified to standard integrals by using an appropriate…

Q: please answer the question and show all of your work

A: Given integral is

Q: dx 6. xVa² - x² X

A: Consider x=asinu. Differentiate the equation x=asinu and simplify to calculate the value of dx.…

Q: Evaluate the improper integral or show that it diverges. (1+4x)e*dx

A:

Q: 33 = 1-

A: Here we evaluate the integral by using substitution method    ∫ dt/(1-3t)7 , u = 1 -3t

Q: Evaluate the integral, if it exists.

A: Given- ∫-11sinx1+x2dx To find- The value of the above integral. Concept Used- The above integral can…

Q: Use a table of integrals to evaluate the definite integral.

A: We have to evaluate the definite integral using table of integrals: ∫03x2+16 dx Rewriting the…

Q: Evaluate the given integral with suitable substitution: (42x + 42) dz

A:

Q: Evaluate the integral by reversing the order of integration. An (6x²) dxdy COS 0.90634

A:

Q: Use the Special Integration Formulas to find the indefinite integral.

A:

Q: Evaluate the integral using trig substitution: ∫√(1+x2 )/x dx

A: The integral function is ∫1+x2xdx.

Q: dx J 3+1 3+ vx

A:

Q: x6 dx V x14 - 3

A: ∫x6  dxx14-3 On simplification, we get ∫x6  dxx14-3=∫x6  dxx72-32 Now put, x7=t⇒7x6=dtdx⇒x6  dx=dt7…

Q: Evaluate the integral J*(x*-1)°dx by using substitution.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 16 In xp (x^ +C

A: Topic:- integration

Q: In 3 | (1– x)e"dx X — х In 3

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 7 In(x) dx XV 5 + (In(x))²

A:

Q: Evaluate the integral: J sin (4x) dx.

A:

Q: Evaluate the integral. π/4 Jo 0 sin5(x) dx

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

Q: Use the Method of Substitution to find the indefinite integrals: t3et“ dt dx x VIn x

A: The given integral,a) ∫t3 et4 dtb) ∫9xln x4dx

Q: evaluate the integral or state that it diverges.

A:

Q: evaluate the integral from 0 to 3, x^3 dx/ sqrt 9+x^2

A:

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.