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

Q: Use a Table of Integrals to evaluate the integral. sin(3x)dx

A: To evaluate: ∫e6xsin3xdx Let, I=∫e6xsin3xdx Integration by parts states that…

Q: Use any method to evaluate the integrals ∫cot x/cos2 x dx

A:

Q: Evaluate the integrals ∫sec2 x tan2 x dx

A:

Q: Use the Table of Integrals to evaluate the integral.

A:

Q: Use a table of integrals to evaluate the definite integral.

A:

Q: x arcsin(x²) dx;

A: Given that: *∫sin-1u×du=u×sin-1u+1-u2+C The given expression is, ∫x×sin-1x2×dx Let,  x2=u,…

Q: Evaluate the integrals ∫tan5 x dx

A: I=∫ tan 5x dx =∫Sin 5xcos 5x dxLet cos 5x=t-5 sin 5x dx=dtsin 5x dx=-dt5

Q: Evaluate the integrals ∫sec3 x tan x dx

A: To find the given integral.

Q: Use the Table of Integrals to evaluate the integral.  ∫ Sin-1 √x dx

A:

Q: Use a Table of Integrals to evaluate the integral. 5x sin(4x)dx

A:

Q: Evaluate the integrals ∫sin4 2x cos 2x dx

A: I=∫ Sin4 2x Cos 2x dxLet Sin 2x=t2 Cos 2x dx=dtCos 2x dx=dt2

Q: Use the Table of Integrals to evaluate the integral.  ∫ x Sin( x2) Cos (3 x2 )dx

A:

Q: Solve the integral by using integration techniques

A: We have to solve

Q: Evaluate the integrals ∫sin3 x dx

A:

Q: use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

A:

Q: Evaluate the integrals.

A:

Q: Evaluate the integrals ∫sin5x/2 dx

A:

Q: Evaluate the integrals

A:

Q: 5. Evaluate the integral by using trigonometric substitution. x2 dx J Tx2 - 25 Vx² –

A:

Q: Evaluate the integrals ∫cos5 x sin5 x dx

A: Given integral:

Q: | tan(3e)

A:

Q: Use the Table of Integrals to evaluate the integral.  ∫ sin2x cos x ln(sin x) dx

A: We have to evaluate ∫sin2x cosxlnsinxdx Let substitute  t=sinx ⇒dtdx=cosxdt=cosx dx Substituting…

Q: Evaluate the integrals ∫sin 2x cos 3x dx

A: We have to evaluate ∫sin2xcos3xdx. We know that 22sinA cosB=sinA+B+sinA-B Therefore,…

Q: cOs x In(sin x) dx

A: Given,  ∫cos x ln(sin x) dx

Q: Use the Table of Integrals to evaluate the integral.  ∫ sin6  2x dx

A: Consider the provided integration, ∫sin62xdx Find the value of the provided integral. Apply the…

Q: Use a table of integrals to evaluate the definite integral.

A: Given: I=∫0π2xsin2xdx for evaluating given integral, we use integral by parts theorem according to…

Q: Use a table of integrals with forms involving a + bu to find the indefinite integral ∫ 2 / x2(4 +…

A: Given:I=∫2x2(4+3x)2dxTo find:The value of the integration I=∫2x2(4+3x)2dx

Q: Evaluate the integral. integral 0  to pie /2     sin 3x  cos 2x dx

A: Consider,

Q: Evaluate the integral 5x sin (x2) dx by using any methods.

A:

Q: Evaluate the integral.

A: Given ∫0π2sinθ·ecosθdθ

Q: Evaluate the integrals ∫sec x tan2 x dx

A:

Q: Use any method to evaluate the integral. cot 2x xp- sec 2x

A: Here in this question given that a integral problem .  We use the integration formula and help some…

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) [ 7…

A:

Q: evaluate the integral using the methods covered in the text so far.

A:

Q: Evaluate the indefinite integral by using the given substitution to reduce the integral to standard…

A:

Q: evaluate the integral using the methods covered in the text so far.

A:

Q: please answer the question and show all of your work

A: Given integral is

Q: find the indefinate integral of sin^5(x)cos(x) dx

A: I = ∫ Sin5x  Cos x dxLet Sin x = tCos x dx = dt

Q: dx 2. S: 3 cos x+2 sinx-5

A: Evaluate the integral ∫dx3cosx+2sinx-5

Q: Evaluate the integrals ∫sec2 x tan x dx

A: Given:∫ sec2x tanx dx

Q: Evaluate the integral of sin(4x) cos(3x) dx

A: We have to use 2sinAcosB= sin(A+B)+sin(A-B) formula to simplify first.

Q: Evaluate the integrals. ∫(tan-1 x)5/(1 + x2) dx

A: We have to evaluate the integral: ∫tan-1 x51+x2dx This integral will be solved by substitution…

Q: Evaluate the integral by using multiple substitutions. x² sin (9x2) Vcos (9x³) dx COS 25)

A:

Q: Evaluate the integrals ∫cos3 2x sin5 2x dx

A: Evaluate: ∫cos32xsin52xdx

Q: Evaluate the integrals ∫(sec θ tan θ) √(1 + sec θ) dθ

A: Our Aim is to evaluate the integral given below:-∫sec(θ) tan(θ)sec(θ) +1dθ  -(i)

Q: Evaluate the integrals ∫(tan x)-3/2 sec2 x dx

A:

Q: Evaluate the integral using the substitution rule. 7/3 sin(x) dx cos?(x)

A:

Q: Evaluate the integrals ∫sin3 x cos3 x dx

A:

Q: sin' (2x) cos (2x)dx =

A:

Q: 3. Evaluate integral by using a basic substitution: S x² sin xdx

A: Given: ∫x2sinxdx To evaluate: The 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.