) = 31 + 3E, = 2E2 = 3, =4E, = 5| and A = 1| Find Ef(x) Ax! The sum in part (a) approximates a definite integral using rectangles. The Ef(x) Ax= D implify your answer.) Find the definite integral that is approximated by the sum in part a. dx

Q: 9x²9x + 54 x³ + 3x 1² dx

A:

Q: sec²(/T+1) dr. 9.

A: To integrate ∫sec2x+1xdx Substitute u=x+1 Then         dudx=ddxx+1       =ddxx+ddx1       =12x12-1+0…

Q: 17) Calculate the indefinite integral S-5dx √4-16x² 16) Evaluate the definite integral Š - 0 3…

A: 16).17).

Q: Evaluate the indefinite integral 4 dx 15x + C

A:

Q: QUESTION 2 a) Evaluate the integral | dx (x-5) +5 b) Show that 5+4x - x² = 9-(x-2) by completing the…

A: (a). From the given problem: I=∫5x-52+5dx   ...1 Let, u=x-5So,ddxu=ddxx-5dudx=1-0du=dx

Q: 5. म 4-93ो डे (A-कर कर Cos (4-3x) dx

A: ∫sin54-3xcos44-3x dx=∫sin44-3xcos44-3x sin4-3x dx=∫sin24-3x2cos44-3x sin4-3x dx=∫1-cos24-3x2cos44-3x…

Q: -3v3 dx V9+x?

A: Evaluate the intregal

Q: 2 8 dx 1 x(x²+2)² 3.

A: Solve the following integral

Q: d Calculate the integral 2r -x

A:

Q: Solve the integral

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.