(b) Evaluate the integral using by parts (* sin 2xdx formula:

Q: c) f t√t + 4 dt e) S X 25+16x² dx 25+16x² d) f 25 dx x (19wansoy dilquma) dx 25+16x² f) S

A:

Q: tan Find -dr using integration by parts.

A:

Q: find integral of sin-4x

A: Given: -

Q: Determine ∫2x(x^2 + 5)dx by making a substitution. Then, determine the integral by multiplying out…

A: Evaluate: ∫2xx2+5dx

Q: y(t) +4 et"y(t – v)dv = 3. Let Y(s) denote the Laplace transform of y. (a) Apply the Laplace…

A:

Q: Find the integral ∫dx/sin22x without using a substitution.

A:

Q: Use a substitution method to evaluate the integral

A:

Q: Scot(x)dx

A:

Q: find integral of sin2xln(tanx)

A:

Q: Use Table shown to rewrite as the difference of two integrals.

A: Given integral, ∫162x3-4xdx          ...(1)

Q: 2e-2x – 3e3x 14. - dx e-2x + e3x

A: deaxdx = a.eax ∫1u du = lnu +C

Q: dr Vr - 9

A: Given: I=∫drr3-9   ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫1ax+bdx=1alnax+b+C

Q: 3 4. y sin³ 4x cos 4x =

A: The given function To find:-The integral in terms of sine function

Q: 21.3 xdx V16 - 9х4 0.

A: We to integrate the given integration.

Q: elnx 8) fex dx g) √1-e²t dt (Hint: let u = e¹) h) fx dx dx (let u = x¹/2)

A: g)∫elnxxdx

Q: Find the integral ∫dx / sinx+cosx+1

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.