(e² sin*(2r)' 21² +1 , y = In

Q: An ice cream cone can be modeled by the region bounded by thehemisphere z = √8 − x2 − y2 and the…

A: (a) Sketching the ice cream cone in 3 dimensions:The hemisphere z=8−x2−y2​ represents the upper half…

Q: 2)( L[ (1 – 27)' sin 2r.dr)) =

A: Using the formula

Q: The y' of the given function is (1–2 sin? 4x) y

A:

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: sin 0 cos Od0 -u'du FC = - 1 cos“ 0 + C 19.

A:

Q: g(x) = 4ecoN " sin x, (0, ] COS

A: Given data:   The given function is: g(x)=4ecosxsinx The given interval is: [a,b]=[0,π].   The…

Q: +3x2 B) Find dy/dx if : (****")) (v)² = sin (cos³

A: Differentiation chain rule

Q: x+(1/x)=2 cos theta , then show that x2+(1/x2 )=2 cos2 theta

A:

Q: (b) S tan3 x sec² x dx c) S sin³x cos5 x dx

A: The explanation of the solution is :

Q: sin(2w)dw =

A:

Q: Solve d²y dx² cot x dy - sin² dx sin² x.y = cos x - cos³

A:

Q: what is y' of y=sin-1(cos x)

A:

Q: 1 |Leax sin(bx)] eax [a sin(bx) – b cos(bx)]+ C * Using the formula dx = ах a² + b². Sie [e-8x…

A:

Q: 7) {(1- sin° 31)- cos3t dt 8) | t in’ (5x)· sec´ (5x) dx

A: 7) I=∫1-sin2 3t·cos 3t dt  ……1

Q: /2 sin aVT-2 cos r dr /3

A: To find the given integration

Q: C- Find f' of the following: 1) √2x³-2² + In ² 2) 3xe³r+1 3) sin ¹(³).

A:

Q: 7/4 (sec² x – sin x)dx

A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

Q: -S * sin ´sin sin (e*) dx

A: we have to integrate

Q: 7 (1 + sin² x) = e 2" sin 2.x, y(0) = 1 X 7) dx

A: This equation solve by separation variable

Q: ~|J O 1- Cos 2πTX) dx L x (1. 2

A:

Q: dy - (1+x)у -ху? .2 1.) х- dx

A:

Q: 3 + 4x sin (xy') dy dx Enter an algebraic expression [more..1

A: Given query is to find the derivative of the expression.

Q: Differentiate y = (ln r)tan 2x

A: We have to differentiate; y=lnxtan(2x)  taking natural logarithm both of sides;…

Q: 2 show that sinz-- i\n(izz√1-2²)

A:

Q: (1+siny)[1+sin(-y)]=cos2y

A: Given:

Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

A:

Q: 5. (a) 2e' sin? (b) e cos ?1

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.