80 K 19. GIVEN: K = P, J + mxP = 180. %3D PROVE: KL || JP. J

Q: Evlute y" +1

A:

Q: 4. a B A(0,e) B( = /2, 1/2) 7 ((0,1) Find the hyperbolic lengths a, b, and c. a Find coshlal cash…

A: Given: The points: A0,e, B12,12, C0,1.   (4.) To Find: The hyperbolic lengths a, b and c. (5.) (a.)…

Q: a) Find the general solution for UTM dy TM dy +2- dr? dr (1+f) UTM (77 +1)xz² = fip +

A:

Q: 6. Given : 23 24, RT ST 3. Prove: HR ES 2. R

A:

Q: 2 6 f sec 0 tane de

A: To Find : ∫sec2θtan6θdθ

Q: 1f itwas x25ect, yatunt prove Thut dy

A: Simple derivative

Q: Q3. If w = f(u, v) , u = cosx and v = sinx, show that: d?w v² funu + u? fov – 2uvfuv – ufu – vfp %3D…

A:

Q: dy Q3) Find dx for 3(x? + y?)2 = 100xy %3D

A: The given equation is 3x2+y22=100xy.

Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x :x > 5}. Find h. D'n (AUB)

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.