Consider the following integral dx After making the trigonometric substitution r = 3 sin 0, which does the integral become

Q: 4. Evaluate the trigonometric integral. sin³ 0 cos? 0 de 3

A: Given that,

Q: Use the substitution a = 2 sect to evaluate the integral dz

A:

Q: */2 Cos Jo

A:

Q: (a) Choose the appropriate substitution for a in terms of using the above (b) Determine dx in terms…

A:

Q: Q2: find the integral of trigonometric function cos sin* dx

A: Given the integral is ∫0πcos5xsin4xdx

Q: d Use the Product Rule to find (and simplify): [sin'x]

A:

Q: 11. Find the definite integral of S, 2 sinx 1+cos x dx : A. In (1+ cos x) В. 2 In 1 C. In 1 D. In 2

A:

Q: dx 4. Evaluate correct to 3 decimal 3-2 sinx places. (10)

A: See the details solution in below

Q: | sin 3x sin 6x dx

A: Given: ∫sin3xsin6xdx

Q: Evaluate the integral.  integral sin 6  x  dx

A: Given ∫sin6x dx We use sin2x=1-cos2x2cos2x=1+cos2x2

Q: sin I 3 1+2

A: We can use the concept of odd or even function in order to solve the given problem.

Q: (12 3 sec* 3xdx 15.

A:

Q: Consider - Vx2-9 x3 dx. Using trigonometric substitution, what is the integral form in terms of 0?

A: To solve a certain type of complex integrals we usually simplify them using basic trigonometric…

Q: 1. Evaluate the integral. S. a) t sin3tdt b) / V1+a* dx

A: (a) Given: ∫0πt sin 3t dt Apply integration By part : ∫I.II dx=I∫II dx-∫ddxI∫II dxdx Take: I=t 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.