Find the integral. dx 7/3-3x2 +C O b 2x2 육x기3-2x-2.c O d + 2x

Q: Evaluate the integral. 6. 6 cosh (x) dx X, 4

A: Let x=u Differentiating both sides with respect to 'x', we get ddxx=ddxu12x=dudxdxx=2du

Q: Evaluate the integral by completing the square: dx 4x2 + 4x + 10

A:

Q: Evaluate the integral by making the substitution u = x5 – 6.

A: Given∫x4(x5-6)6dxSubstitute x5-6=uDifferentiate x w.r.t u5x4dx=dux4dx=15du

Q: Evaluate the integrals

A: Given: The integral

Q: 3x?dx 10. S 9x6-12x3+4

A:

Q: Evaluate the integral ∫dx/1+2x2.

A: Given :

Q: Find the integral

A: To evaluate the integral: ∫x25-9x2dx Solution: ∫x25-9x2dx…

Q: 1= [3y/7-3y° dy

A:

Q: Evaluate the integral by completing the square: dx 4x + 4x +5

A: Solution: The objective is to find the given integral

Q: Evaluate the integral:∫xe−2xdx

A:

Q: 12sin3xcos7x dx

A:

Q: Evaluate the integral: 9e3x dx e3x Ve6x - 25

A:

Q: Find the Integral by using the substitution method.  x(7-x^2)^1/2

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

Q: Evaluate the integral. S (4x' – - 3x? + 2x) dx

A: The integration of the term 4x3-3x2+2x limit from 1 to 2.

Q: Evaluate the integral. | 7x secx°dx

A: Given, ∫7xsecx2 dx  We have to evaluate the integral

Q: Evaluate the integral. dx 2x – 1

A: Let 2x - 1= u hence, 2dx = du Or, dx = du/2 when x = 2; u = 2 x 2 - 1 = 3 when x = 5 ; u = 2 x 5 - 1…

Q: Evaluate the integral: ∫ (2x2 − 3x)2 dx

A: ∫(2x2-3x)2dx

Q: 19. (+ 2x 4) dx

A: ∫ af(x)±bg(x) dx = a∫f(x) dx ± b∫g(x) dx . ∫xn dx = xn+1n+1+C

Q: Find the integral. хебх dx (6x + 1)2

A:

Q: aメ+ 3 dx 2+4

A:

Q: Evaluate the integrals ∫ 1/x6(x5 + 4) dx

A: Integration : ∫1x6(x5+4)dxWe need to perform partial fraction decomposition:

Q: evaluate the integral.

A:

Q: Calculate the integral ∫dx / √(x2−8)3.

A:

Q: メナー Aト 2.

A: Let's find.

Q: Evaluate the integral.

A:

Q: dx 5x2 + 16

A:

Q: Evaluate the integral. -1 4 6y5 dy + -2

A:

Q: Evaluate the integrals ∫(3x2 - 4x + 7) dx

A: ∫3x2-4x+7dx Formula ∫xndx=xn+1n+1+C

Q: 2. Find the integral Jsec dx

A:

Q: Evaluate the integral ex /2e-2x – 3e2x xp-

A:

Q: Evaluate the integral 9x² √x² + y² dzdy dx

A: Given problem:-

Q: dx 4x2 + 9

A: Use substitution.

Q: Evaluate the integrals

A:

Q: Sx³(a² + x²)î dx

A: We will solve the problem.

Q: Find the integral. dx 3- 2х A 글메3-2x+C B -글 미 3-2지+ C c) 2 In 13 - 2x| +C D) - 2 In 13 - 2x| +C

A:

Q: Evaluate the following integral. ∫ 2z5e1-z dz

A:

Q: Evaluate the integral dx 2xx - 3x?

A: To find: The integral ∫dx 2xx3-3x23 Concept used: ∫1-v2+1dv=lnv+12-lnv-12

Q: 2z+8 (z+7)4 dz

A:

Q: Evaluate the integral. dx 2x

A:

Q: Compute the integral by algebraic substitution:  ∫3x^5√16-x^2 dx

A: The given integral is: ∫3x516-x2 dxLet, I=∫3x516-x2 dx⇒I=3∫x516-x2 dx    -1

Q: S 3xe*dx

A: Given problem :- ∫ 3xex/2 dx

Q: Evaluate the integral: =°/1+ 64z*dz

A:

Q: Evaluate the integral dx (7x + 6)2

A:

Q: Find the integral ∫dx / 3sinx+4cosx.

A:

Q: Use integration by parts to evaluate the integral. | (In(3x))*dæ- 8, +C

A: The given integral is ∫(ln(3x))2dx. Let  3x=u. Differentiate both sides.    3dx=du⇒dx=13du…

Q: Evaluate the integral |-1|2 – 4z| de

A:

Q: Evaluate the improper integral : 6be 8z" dx

A: Note: As per our guideline we are supposed to answer only one question. kindly repost the other…

Q: Evaluate the improper integral : (* 6xe-3x°, dx

A: We need to evaluate the following improper integral I = ∫-∞∞6x5e-3x6dx…

Q: Evaluate the integral |- 5x + x3 - 2 x5 dx 3

A: Topic:- integration

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.