Find the definite integral of: * 27 cos -w ) sin w) dw. O - 1/2 O - 1/12 О 12 2

Q: 6. Evaluate each indefinite integral Sx• cos (x² + 3) dx a. b. Sx-1 dx

A: Integration by substitution, and Using trig. Identity

Q: Csin $ 3 y cos*3 ychy

A:

Q: 10. Prove that 7/2 sin 8 cos (cos a cosec 0) de =- (1-cos a). CO TE/2-a

A: We will use the Differentiation under Integral sign method, to solve the problem.

Q: If sin 0= and is in QII, cos is equal to COS A 4/5 5/3 -4/5 D -5/3 B.

A: Given Sinθ=35We know sin2x+cos2x=1Upon substituting:cos x=1-sin2x        =1-(35)2

Q: 53. So 0 ex sin x dx

A:

Q: Evaluate the following trigonometric integrals: 1+cos 2 0 L, V4 – x2 dx Hint: Put x = 2 sin 0 and…

A: We evaluate  this integral of trigonometric ratios by using substitution method and basic…

Q: Evaluate the following integral

A: To integrate

Q: 2. cos z sin r dr

A: Consider the given integral: ∫cosx·sinx·dx We know that, 2cosx sinx=sin2x Hence,…

Q: Use the identity sin? x = 1– cos²x to write f sin?x cos?x dx a sum of two integrals and then…

A: To apply the reduction formula, substitute sin2x=1-cos2x, in the integral and simplify.…

Q: We apply one of the Half-Angle Formulas to simplify the integral cos (5æ) da. VWhat is the resulting…

A: We know the identity  Cos(2x)= 2cos2(x)-1

Q: Which of the following is one of the correct steps to evaluate |dt to obtain the correct indefinite…

A:

Q: 2+ sin x dx. 3 - cos x

A: This question is about application integration

Q: Evaluate the following integral: tan dx x2 b) (a/3 In(tan x) dx sin x cos x

A: Solved below

Q: tan ( tan3x) dx Evaluate: cos?3x

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.