11. Rules of Definite Integrals: If f(x)dx = 12, S." f(x)dx = 6, and "f(x)dx = 4, find the following: a) b) o) 16s)-4]är. d)

Q: A5. The value of the definite integral dx is b) - 8 c) 24 d) 1.5

A: We have to find the value of the given definite integral.

Q: tid Q3. Evaluate the following integrals 1) cothx.csch2x. dx (50-3x - √x+1+73 44x

A:

Q: Solve the following integrals: a) SVI+ - v2 dx b) Sxcos 2x? dx

A:

Q: (Sy?-8X46) dx =?

A: We need to evaluate ∫045x2-8x+6dx

Q: Calculate a) ∫x ln x dx. b) ∫cos (2x) dx c) ∫ 2x +1 dx        x² - 1 d) ∫20   (x − 1) 25dx

A:

Q: a. / (3z² + 6) (z² + 6z)° dz 7– 2 dz b.

A:

Q: + 4x – 2) dx -1

A:

Q: 2x4 1+x² a) [: dx b) [ cos² cos² 2x dr

A:

Q: B. Given e" (1+ e*)-$dx. Let u = (5). Then, du = Now, we can write ----- ---- the integral as /…

A: Given that       ∫ex(1+ex)-1/3 dx .

Q: Given [[(a² – x² – y² ) dxdy over the positive quadrant of the circle x² +y? = a² . Find the value…

A: We are given the Integration: ∫rs∫pqa2-x2-y212dx dy Over the positive quadrant of circle: x2+y2=a2…

Q: :)dx = -2 and | g(x)dx = 9 to evaluate the definite integral [f(x)-9g(x)]dr. Use the values

A:

Q: Q3) Use substitution to find the following integrals a. f sec²x √tan x dx b. dx x3 Sa (1+x4)5 C. csc…

A:

Q: Q3)Evaluate the following integral by using Trigonometric Substitutions Method. dx = √√√9x² +9 y =

A: Let's solve integration by using trigonometric substitution.

Q: dx (§5.7, Q28) Evaluate the indefinite integral: (x – 9)5"

A: step 2 complete solution

Q: 3- Find the value of integral by using the Gauss quadrature (three points) I = -dx x+1

A: We can find the approximation of the integral of a function over a closed interval  usingthe Gauss…

Q: dx dy dz

A:

Q: Find the indefinite integrals below. a) S 12x³ Vxdx dx x³-7 b) S c) S 9e0.2x dx

A: We have tofind the indefinite  integrals.

Q: 5. Select the correct value of the definite integral (√x + 1)dx from the below: a) 81/4 b) 331/12 c)…

A: