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: Evaluate the definite integral | 8 sin(æ)dæ

A:

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

A:

Q: [ cos² 2x sin² 2x dx

A:

Q: sin ede 1- cos e 8.

A: The integral of sinθ is given by -cosθ and the integral of cosθ is given by sinθ. The basic formula…

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: (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: dx x' +9 2. Use an appropriate trigonometric substitution to rewrite as J(a simplified trig function…

A: Solution: The objective is to find the value of given integral

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.