tan(x)dx, Ind: u = cos(z)

Q: Use the indicated substitution to evaluate the integral.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) A) x cos(2x) dx B)e6θ sin(7θ) dθ

A: here we evaluate the integral      (A)   ∫ x cos (2x)dx     (B)  ∫ e6θ sin (70) dθ

Q: Use integration by parts to evaluate the following Integral S3 cos x? dx

A:

Q: ** Using the substitution y=x, the integral eln24 evx dx is the same as or equal to

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: b. I = S(1+ sin x)5 cos x dx

A:

Q: Use the specified substitution to find or evaluate the integral.

A: To evaluate the given integral using the specified substitution.

Q: Evaluate the integral. (Use C for the constant of integration.) | 3x2 cos(mx) dx

A:

Q: use the indicated substitution to evaluate the integral.

A:

Q: evaluate the integral in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a.

A:

Q: 2. Use a substitution to change the integral into one found in the table of integrals, then…

A:

Q: Using an appropriate substitution, 8tan-1x the integral J dx equals: 1+x2

A:

Q: I = S(1+ sin x)³ cos x dx

A:

Q: Evaluate the integrals using the indicated substitutions.

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: A. Evaluate the following integrals. ´sec² 0' dx 4. tan 0

A: The integration of the integral is sec2(theta) /tan(theta).

Q: S sin x e cosxdx

A: The objective of the question is evaluate the given indefinite integral using substitution method.

Q: Use the integration by parts to evaluate the following integral by assuming u = COS 2 dx (cos a + a…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) sin (0) cos (0) de

A:

Q: Evaluate the integral. (Use C for the constant of integration.) sin3(0) cos“(0) de

A: Here,

Q: Sx²e2x*dx `x²e?

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Evaluate the integral. (Use C for the constant of integration.) s¯¹(x) dx COS

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) sin…

A: see below the calculation

Q: Use the indicated substitution to evaluate the integral.

A: Given:           ∫012x21−x2dx,  x=sinθ

Q: Find the integral for the following : dx 2- fe-*sec? (ne-*)dx 3- Sdx ZVI+2x 1+e*

A:

Q: Derive the formula by using integration by parts on the left-hand side. (Assume n > 0.)

A: Given:

Q: Evaluate the integral in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a:…

A: given,         A=∫x2cosx3+1dx

Q: sin x cos? x dx

A:

Q: Evaluate the integral cos(x?) dæ dy by reversing the order of integration.

A:

Q: dx '1 x[13+ln(x²)]

A:

Q: Use the substitution technique to determine the following integrals:

A:

Q: Evaluate the integral. (Use C for the constant of integration.)  e−θ cos(6θ) dθ

A:

Q: Use integration by parts to evaluate the integral.

A: Apply integration by parts,

Q: Use reduction formula to evaluate the given integral xe" dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 9 sin?(t) cos“(t) dt

A:

Q: Using an appropriate substitution, the integral f e cos(e* + 1) dx is equal to:

A:

Q: First make a substitution and then use integration byparts to evaluate the integral.   ∫Cos √x dx

A: Given: I=∫cosxdx for evaluating given integral, we substitute x=t…

Q: Use Simpson's rule to find the value of the following integral -3x² dx -0.9 e 0.1 where n=4

A:

Q: Using the Simpson's rule for multiple integrals, evaluate the following integral; | Vx +y) dx dy

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Consider the expression 3x2-2=u. The power rule of differentiation states that d dx(xp)=pxp-1, where…

Q: f(cos*x- sin *xkx *a

A:

Q: ∫dx/(sinx)(cos2x)

A: Integration is calculated using basic properties.

Q: For the given integral dx sin-cot- 2 2 what is u?

A: Take u=x/2 then integrate it

Q: To evaluate the integral Vx2 + 4x + 5 dx using a trigonometric substitution, use the substitution…

A: As we know that 1+tan2x=sec2x

Q: a) Evaluate the integrals using appropriate substitutions. dx Sine i) S ii) S de Cos? 0+1 1+16x?

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The best substitution to use for the integral sin z V1+ cos z dx

A: when we substitute, u = 1 + cosx then the value of du = - sinx dx

Q: Apply the method of substitution to integrate the following integrals: dx I = ; a. Va²-x² b. I = [(1…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 5 cos?x sin 2x dx

A:

Q: Evaluate the integral I = x + cos()dx using two point and three point Gaussian Quadrature and…

A: We have I=∫-11x2+cosx2dx First, we find the exact solution. Consider:…

Q: The given integral is Te-x³(-3x²)dx. Let -x. Now differentiate u with respect to x. That gives U =…

A:

Q: Use the Method of Substitution to find the indefinite integrals: t3et“ dt dx x VIn x

A: The given integral,a) ∫t3 et4 dtb) ∫9xln x4dx

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.