dx Q3 a. Evaluate the integral X - x

Q: c) Evaluate the following integral | dx. x2 +6x+10

A: x2+6x+10=x2+6x+9+1x2+6x+10=x2+2*x*3+32+1    (a2+2ab+b2=(a+b)2) x2+6x+10=(x+3)2+1

Q: dx b. (x² + 1)(x² – 2x + 1) -

A:

Q: -x + 2 dx . x2 + 2x ate the integral

A:

Q: g+y= 쓸 - zxe - 5

A:

Q: 3 2—х ∞ Lo dx X¯e

A:

Q: Find the indefinite integral

A: Formulae used: ddxxn=nxn-1ddxC=0∫12xdx=x+C∫1a2+x2dx=1atan-1xa+C

Q: +00 dx -Evaluate the improper integral x (In x)²

A:

Q: O Find the integral f xsec2x dx

A:

Q: X- xe d.x

A: Given :   ∫0+∞xe-xdx

Q: dx. Evaluate the integral / (x² + 1)(^ · x – 2) -

A:

Q: Evaluate the following integral. 1 dx x2 +4 0.

A: Use the method of substitution to evaluate the limit. Assume I=∫021x2+4dxLet…

Q: Evaluate the definite integral. ¤(x² + 7)°dx (b) / z x/1 – x²dx (a)

A:

Q: Evaluate the integral х3 dx x2 +49 х3 dх x2 +49 (Use C as the arbitrary constant.)

A: We substitute x^2+49=t, then the given integral become

Q: Evaluate the integral. | (e7* +3e -x) dx 7X +3 e -X) dx=

A:

Q: Q2 ) Evaluate the integral S*9/x7 + y²) dxdy.

A:

Q: x² = 10) Evaluate the integral S dx, x > 3

A:

Q: 16 – x2 dx - Evaluate the integral: 9x?

A: (A)  x=4sin(θ) (B)  19cot2(θ) (C)  -19θ-19cot(θ) (D)  -19arcsin14x-16-x29x

Q: Evaluate: 2 1 dx x7 The integral is divergent.

A:

Q: Evaluate the integral. 1 (x² + 3)e¯× dx 0.

A:

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

A:

Q: Find the indefinite integrals: x5/2 + 4x + 1 dx a) / ? b) / (a" 6t7 2 + Te' ) dt t3

A:

Q: Q2) Find the integral of: 6 tan*x dx

A:

Q: Evaluate the indefinite integral 5e" dæ S 5e² dx +C

A:

Q: -dx. Q5. Evaluate the integral / Tx² + 1)(X · x – 2)

A: Given  α=5 ,β=8 ,γ=13,λ=2 ,θ=5 , η=3 ,ω=2 . To rewrite the given integration by using α=5 and λ=2 .…

Q: Evaluate the integral. .2 5) t + dx t 1

A: Given,   ∫12t+1t2dx

Q: Find the indefinite integral. (Hint: x² – x-4 ) g6 – 1 dx + C

A:

Q: Q3 - Evaluate the following integrals dx x+V4x2+1

A:

Q: Evaluate the integral x3 dx 2+100 S x3 dx +100 (Use C as the arbitrary constant.)

A: Given,

Q: 7x Evaluate the definite integral : dx (6x2+2)2

A: Given,          ∫017x6x2+252dx

Q: Q1 - Evaluate the following integrals ii. S dx Jo ix-1|

A:

Q: dx Q24: Find the integral of f (x+1)(x2+1)

A: The given integral is ∫1x+1x2+1dx.

Q: Evaluate the integral. a dx 2 a > 0 (a² + x²)3/2' V2 92

A:

Q: Q6. A: Evaluate the integrals: sec x dx dx 2) L, | VIn(secx+ tan x) -2 (4+x²)3/2

A:

Q: Q3 - Evaluate the following integrals i. S7 xp V9-x2

A: Use substitution method

Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: Q2) Evaluate the integral x3 dx 3 a *0.

A:

Q: Q18: Evaluate the definite integral: 4x dx V1 + 2x²

A: To find the definite Integral  Substitute 1+2x^2 = t and change the limit accordingly

Q: Q4. Find the integral of the following functions x dx (x-1)(x2+2x+1)

A:

Q: - 03. Evaluate the following integral: (1 – x - 4x + 2x)dx -2

A:

Q: Q(1) Find the integral of Vx² – 16 dx

A: Use substitution method to find its integration.

Q: (a) Evaluate the integral [x (x* -1) ´dx by using substitution.

A: To evaluate the given integral ∫x3x4-12 dx by using substitution.

Q: dx. ot Find the indefinite integral x4 = xp

A:

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

A: To evaluate the given integral

Q: a) Find the integral 3x7 dx dy . Vr – x2 -

A: Given, the integral is Here y = 0 and y = 1 and x = Öy and x = y2.

Q: Q1 - Evaluate the following integral: J (2x-3x+2) dx (x-1)2 (x-2)

A:

Q: 2. S*3*+2 dx x+2

A:

Q: Q23: Find the integral of f x In(x) dx.

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

Q: Find the integral [(x** +(-1)°x*!) In((a+2)x)dx b+1 с+1

A: The integral has been solved n attached in the second step.

Q: Use substitution to find the indefinite integral. P(p + 9)°dp

A: We have to find given integral.

Q: the integral (dx)/(xsqrt4x2+1)

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.