and find If f and g are continuous functions with [3f(x)dx = 36 [*5g(x)dx = -21, [*{3g(x) – 4ƒ (x) — √/9 – (x − 1)²]dr.

Q: 2. . If f(x) dx = 4 and 3g(x) dx = -9, evaluate [² [3f(x) + g(x)] dx

A:

Q: Given that (a) (b) Prx [ FLX f(x) dx = 3 and f(x) dx 2 [²(x [²Px) dx - [Px) dx f(x) f(x) f(x) dx =…

A:

Q: Find the c value satisfying MVT for f(x) = 3x² + 2 in 1 < x < 5

A: Given: fx=3x2+2 in interval 1&lt;x&lt;5

Q: If f(x) is continuous on (-10,-3)such that, -10 -3 -10 I f(x) dx= 35; f(x)dx=71 find f(x)dx -5 -5 -3

A: In this question give that f(x) is a continuous function (-10,-3) find value of integration. Here i…

Q: [x²√1-x² dx

A:

Q: dx -= In[F(x)]+C. What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) A + - B 6. + 3 D + 6 + -15 -15 -15

A:

Q: x+3 4) Evaluate f dx x+1

A:

Q: 2. (a) Define what it means by for y = f(x). %3D

A:

Q: Let f (x) be equal to -x + 1 for x < 0, equal to 1 for 0 < x < 1, equal to –x + 2 for 1 < x.…

A: To evaluate the integral

Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: Find the domains of h(x)=1/(x3+1)1/3.

A:

Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

A:

Q: (x² for x < 2 Evaluate: g(x)dx where g(x) =16 – x for x 2 2

A:

Q: dy Ex2: find for the following functions: dx a) y = (x² + 1)5 b) y = [(5-x)(4- 2x)]? c) y = (2x3 –…

A: According to guidelines we should have been able to solve only three subpart of the question

Q: (c) [ √4x² X -dx

A: The given integration is

Q: Suppose f: R → R is a function such that for all x, y ≤ R, f(x + y) = f(x) + f(y) and f(xy) =…

A:

Q: 3 7) Evaluate: f(-x² + 4x − 1)dx 1

A: Given, ∫13(-x2+4x-1)dx

Q: 2. For f (x) 1, g (x) = 1 + Vx, find the domain and range of f / g, and g/f

A: Given: fx=1, gx=1+x

Q: Differentiate. y = In [(x + 4)(3x- 2)(5 – x)] d In (x+ 4)(3x – 2)(5- x))] = || dx

A: We have, It is known that the derivative of ln(ax) is, and derivative of the function of u.v form…