Use the identity sin? x = 1– cos²x to write f sin?x cos?x dx a sum of two integrals and then evaluate using the reduction formula.

Q: Integrate and use walli's formula. let x=sintheta

A: Given integral, ∫011-x252dx

Q: Integrate the following expressions: Sex-e (2x – e*). dx !! (x + cos2x). dx "/2 X cos2x.dx

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Q: -3RT/2 b. Smt cos³x sinx dx

A:

Q: Write ∫ tan2k+1 x dx, where k is a positive integer, in terms of ∫ tan2k−1 x dx.

A: Given integral is ∫tan2k+1dx. Rewrite the above integral as follow.…

Q: Use the method of substitution to evaluate | 2x cos x? dx.

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Q: Simplify the equation: sechx + sinhx tanhx cosh z cosh a sechx 1+ sinh 2 cosh z

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Q: /9-x² dx. Use trigonometric substitution. x2

A: This question is related to indefinite integration, we will we will solve it using given…

Q: c) Evaluate Ssin 3xcos 4x dx by using integration by part.

A: Given integral is: I=∫sin3xcos4xdx Simplifying it:…

Q: 3. Find each definite integral: A. S(x- 3x) dx | -1 B. ( 2cosx + 2sinx dx

A:

Q: Find the area enclosed by one leaf of the rose r = 12 cos 3θ. Please go into detail when explaining…

A: givenr=12cos(3θ)

Q: dx It sin x-cos x COS

A: To evaluate:∫dx1+sinx-cosx Solution: We know,cos2x=1-tan2x1+tan2x     ...(1)sin2x=2tanx1+tan2x…

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.