serráng Actvity 2. Evaluate the following integrals. Write your answer and solution on a sheet of yellow paper. 1. -3-dx 2. S(5e" - 6*)dz 3. Scot zdx 4. S(2 - csc ? x)dx 5. 1+ sec ?x dr

Q: /3 2 %3D

A: To find: The value of dydx. Given: The equation is y=x35x2+1-23. Formula used: Chain rule of…

Q: 3 Inx S- 2. xV In'x – 4 -dx

A: Consider the given integral ∫ln3xxln2x-4dx Use the substitution method to find the solution of the…

Q: I. Evaluate /4x2 + 4x + 5 dx

A:

Q: Evaluate the integral. (5x2 - 4x +5) dx

A:

Q: 4 dx 0 (52+x²)²' 2)2

A:

Q: 台)。 is dx x²+3x? 2. negative 2 over x cubed 213

A:

Q: .3 1 J2 dx=? x² – 4x+5

A:

Q: S. FInd (4x3 + 3x2 – 2x + 1)dx ·

A: The given integral is as follows:  ∫014x3+3x2-2x+1dx We shall evaluate the value of the integral…

Q: 3 + 2/5x-3 dx. Find 4x+1 - Vez

A:

Q: 7. Use substitution to evaluate ſ 2x(4 – x²) dx.

A:

Q: Integrate .5 X 12 1+x

A: Integration by substitutions

Q: dx /2 4x'

A:

Q: S sec x dx Use Integration by parts to solve

A:

Q: Sx²V4 – x° dx

A:

Q: 3x° Vx² + 2 d

A: Given that a integration of :3x5(4√x2 +2) we solve this integration by using general formulas of…

Q: x?dx V1-x6

A: 1). To evaluate the integral: ∫x2 dx1-x6 Solution: Let substitute t=x3. dtdx=3x2dt3=x2  Substituting…

Q: dx Evaluate J, +6x+10 by dividing the interval into 8 equal parts by using Trapezoidal rule.

A: The integral ∫15dxx2+6x+10. We have to evaluate this integral by dividing the interval into 8 equal…

Q: d x – 2x d -{2x° + x=°] dx 5. dx 6. 7. d 5x-1 dx

A:

Q: l+4vx 15. dx =

A: Given that:∫e1+4xxdx

Q: | V49 + x² dx (7) (8) / - ² x – 4 dx x In x

A: Solve by integra

Q: 2. Determine the following: а. f(8х3 — 2х +9) dx 3 4 6. Vx2 b. S 2-x dx - x2 3

A:

Q: Q.No.3 Evaluate Sx cosec-xdx.

A: Explanation of the solution is given below....

Q: Sts dx 4+x4 4 4 V2

A: ∫54254  x4+x4dxlet   x2=t differntiate on both sides…

Q: dx 1– ex

A: Consider the following integral: ∫ex1-exdx Substitute u=ex2→du=12ex2dx in the above equation:…

Q: x3 – 4x? + 7x – 9 -dx 30. x – 5

A: Find the integration of (x3-4x2+7x-9)/(x-5) w.r.t. "x".

Q: 4. (x? — у?)dx — 2хydy %3D 0

A:

Q: 3X-Y-4 2 . when X=4 i y=l

A:

Q: x³ +4x² + x – 1 dx 2 X 16. .3 2 1 x' + x'

A:

Q: ³+1 2x²5x 3 S dz.

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.