3.) Determine the absolute and relative error that occurs when approximating the integral 32x² dx using three rectangles, each with width Ax = 0.5 and for which the heights are f(0), f(1), f(2) where f(x)=2x². (Hint: the expressed integral is TV while area (Axh) is the AV)

Q: J X √9 - x² dx

A:

Q: Jse the Substitution Method to evaluate the definite integral. * (In x)* dx

A:

Q: 3.) Integrate using an appropriate technique: 24100 dx (show all steps) 4x2 + 24x+100

A: We have to evaluate

Q: Given y = x³ 11 Bac 2³/27x² + 2x, find dy dx H Use the math type b

A:

Q: Calculate the integ ral In (2X +1) dx 2x +1

A: Here we have to calculate I=∫ln22x+1(2x+1)dx

Q: 1 Evaluate the integral S√I+2x f dx

A: We have definite integral  Substitute 1+2x=z2  to make integration radical free as I have done…

Q: 9. /4x – x² dx

A:

Q: SV4-9x2 dx

A:

Q: a) Estimate the area under the graph of  f(x) = 7 + 4x2 from x = −1 to x = 2  using three…

A:

Q: Evaluate the integral of dx/sqrt(x2+4) without using the right triangle method.

A:

Q: (9) 3 ov 1-1) dx

A:

Q: Solve by using u-sub  Find integral  3X/X+4 DX

A: The given integral

Q: Z = 5 X 4 2 -7x+8 d²z dx2

A:

Q: Estimate the area under the graph of  f(x) = 4 + 4x2 from x = −1 to x = 2 using three rectangles and…

A: In this question, we find the area by using the midpoint rule for the given function f(x)=4+4x2 for…

Q: Let F = xyi + xyj + xyzk. Find div(F).

A:

Q: 0 5 X 31x² - 32 do

A: Given, ∫01x31x2-325dx The given integral is solved using substitution method.

Q: dx Vsinxcos3x

A:

Q: dx (x-1)(x²+9)

A: