6. The real trigonometric integral So" do is equivalent to: (2+cos 0)² 1 dz dz (z+z-')ª (2ª +4z+1)? O-(1+i) fc 2141? 0) dz 3z zp: 22+2z+4

Q: a. / (3z² + 6) (z² + 6z)° dz 7– 2 dz b.

A:

Q: .

A: The given matrix is,

Q: Veridy that x - T -Ž ?I ti) e -n4 sin (nx) and 00 -n sin (nx) are equivalent .

A: The Fourier series expansion of x3-π2x in the interval -π to π is given by…

Q: | a 0.24) tan(sin-1x) = b) c) =x d) 1 - x2 3

A:

Q: 12. Evaluate: 212-3V+1 (a) (d) / sec (2) / (b) / sec (20) de dr 1 (e) rVI-1 dr dr 16+9r2 (c) sin t…

A: The given integrals are; (a) ∫2x2-3x+1x2dx (b) ∫01x16+9x2dx (c) ∫0π/6sintcos2tdt

Q: a) 10x-x V10x-dr

A:

Q: Q2.) Using Trigonometric Integrals (Answer one only 1): S sin 5\3 X sec³ x

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Prove that the distance of the roots of the equation sin 0₁ 2³ + sin 0₂2² + sin 031 z + sin 041 = 3…

A: Given equation is  |sinθ1|z3+|sinθ2|z2+|sinθ3|z+|sinθ4|=3 Prove That : The distance of the roots of…

Q: dx sin-1x +c using method V1 – x2

A: Given:

Q: dx cot 3x sin 3x -1/3 sec 3x + C

A: ∫dxcot(3x).sin(3x)=∫dxcos(3x)sin(3x).sin(3x)

Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

A:

Q: (5 + sin r)e 2. If y = what is dy/dr? 12 - 7

A: Use basic identities of derivatives.

Q: D tgy x,y) and fgy (X,4) ) Given f(x,y)= 8x cos (y") find 9. Sin ly") ty 3. 8x 3 > -32x 53 3. 32x |-…

A: Given query is to find indicated partial derivative.

Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

A:

Q: Given SV-x* + 4x + 5 dx. Using trigonometric substitution, what is the integral form in terms of 8?…

A: Trigonometric identities: sin2θ+cos2θ=1cos2θ=1+cos2θ2 If an expression is x2+bx, then we need to add…

Q: 2) [ tan' (-) sec" () dx , 3) | 3) T5x+4 dx, 1) sin-1x dx , tan () sec? V5x +4

A: Since the question contains multiple part we can solve only first 3 for you. If you want any…

Q: i need the answer quickly

A: Given, To prove,

Q: After a proper trigonometric substitution, the following integral the following form: Of…

A: Let us take,  , then our equation change accordingly.we know that    and           and…

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.