3) Evaluate the following definite integral : 8 x V 1 + x dx I

Q: Evaluate the definite integral. 1 ex dx 10 1 + e2x

A:

Q: Evaluate the definite integral 3 10 sin (z)dz

A: To solve the definite integral. Ans=5

Q: (x + 2)² dx X – 2 3

A:

Q: Evaluate the definite integral. 24 V9 + 3x dx Jo

A:

Q: Evaluate the definite integral. (1 – x)² dx

A:

Q: ~3 (x/x+1)dx

A:

Q: Evaluate the definite integral. et dx J1 xyln x

A:

Q: Evaluate the definite integral. 2 X dx 1 + 4x 0

A: Take (1+4x)1/2 = t

Q: Evaluate the integral: |x cosh x² dx sinh x +C 2 x sinh x? +C sinh x? +C x² sinh 2x +C

A:

Q: x' J4-x dx

A: Here we use the substitution 4-x=u to solve this integration.

Q: luate the following definite integral 2 dx J V3 – x + Vx

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: Evaluate the definite integral. 12 | ri+f j|| dt =

A:

Q: Evaluate the definite integral using the given values

A:

Q: 1. (x +2)? dx 5 J3 х — 2

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Evaluate the definite integral. t(5 – t)² dt

A:

Q: Evaluate the following definite integral 6x (1+ x*)³ dx

A:

Q: 1. 2x +3 X+1 T/4 2. tanx secx dx

A:

Q: 20. J 1 (x+25)√√x dx

A:

Q: Evaluate the definite integral. dx | 25 + (x + 4)2

A:

Q: Evaluate the definite integral.

A: Consider the given integral. I=∫-π3π3x4sinx The given function is continuous function in the given…

Q: Evaluate these definite integrals: L, ¢x³ – 3x + 2) dx a. 2e b. S"( cosx – ) dx (Vz – z) dz с.

A:

Q: Use the substitution x = 3 sin t to evaluate the integral f V9 – x² dx. | Note: Use C for an…

A: Given; I=∫9-x2dx   ...1   Use the trigonometric identity; 1). sin2x+cos2x=1 2). cos2x=2cos2x-1 And…

Q: Evaluate the following definite integrals.

A: Given1.∫03xx+1dx2.∫01x(3+x)5dx

Q: Evaluate the definite integral. dx 1+x

A: Evaluate: ∫05x1+xdx

Q: Find the indefinite integral as indicated. J+7° +7) dx 7x dx%3D dx

A: Topic- Integration

Q: Evaluate the definite integral. 1 ex dx 0 1 + e²x JO

A: We will solve the definite integral.

Q: x4 dx (x + 1)(x + 2)²

A:

Q: Evaluate the definite integral. T/2 esin(x) cos(x)dx

A:

Q: Evaluate the definite integral. '4 I 4? + 2)°x dx

A: Let x2+2→u Differentiating both sides of the above equation with respect to x, we get…

Q: Evaluate the following definite integral : 8. 1 + X dx X

A: Given,          ∫08x1+xdx

Q: 6. X1-x dx x dx

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

Q: Evaluate the definite integral | (1+ v) dx.

A:

Q: Determine the following indefinite integral.

A: The given indefinite integral is: ∫1x2-2x52dx Now, use the exponent property 1xn=x-n . ∫x-2-2x-52dx…

Q: Evaluate the definite integral using the given values

A: Given integrals with their values - ∫26x3dx = 320           ..............(1)∫26xdx = 16…

Q: しx(x*+) dx

A: Integration

Q: Evaluate the definite integral. · V½ dx

A:

Q: ²) S₁₂ x ² √ x²+1 dx St 2)

A: The given integral is; I=∫07xx2+13dx   ....(1) As we know the Power Rule: ∫xndx=xn+1n+1+C

Q: Evaluate the definite integral. 25 10e V X dx 0/

A: We use substitution method

Q: Evaluate the definite integral. T/4 | sec(0) de

A: Given: I=∫0π/4secθdθ

Q: Evaluate the definite integral. хVx — 2 dx

A: Use substitutions to integration

Q: Evaluate the definite integral. c (x) tan (x) dx = se 0.

A:

Q: Evaluate the definite integral. '16 9e V x dx

A: Topic- Definite integration

Q: Evaluate the definite integral V9 – x dx 0.

A: ∫05 x9-xdx

Q: Evaluate the definite integral. Sf xVx – I dx

A: Use the substitution

Q: Evaluate the definite integral. Si f (x) dæ, f (x) =3"–(15x³+ 6)/a?

A:

Q: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: dx 3 Vx Vx (1+Vx)²

A:

Q: Evaluate the definite integrals: (a) / (v + dr = 2.x (b) ret“ dr = 2x +1 (c) / dr dx = (고2 + z)3

A:

Q: r1 x³ +1 dx x +1 Jo

A: Definite integrals can be computed using the fundamental theorem of calculus. It states that if…

Q: Evaluate the following integral 1 dx (x – 5)²(x + 3) a

A: We have to evaluate the given integral    The given integral is   ∫1(x-5)2(x+3)dx

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.