21 – In x dx e 1

Q: Find the indefinite integral using the substitution x = 4 sin(8). (Use C for the constant of…

A:

Q: dx I = a² +x²

A: Given query is to find integration of the expression.

Q: Find the exact value of the definite integral below, using the substitution u = x - 1²/1. X (√6+√2)…

A:

Q: Explain why each of the following integrals is improper  integral 1 to 2 x / x-1 dx

A:

Q: 1. Evaluate the following integrals using appropriate methods and simplify your answers. (a) x*e* dx

A: To Determine :-  The given integral is : (a) ∫ x3 ex2 dx

Q: sin(6x) Vi? +4 dt 7

A:

Q: In the given equation as follows , use a table of integrals to evaluate the definite integral :-…

A: Simplification of the function helps to integrate the given function. The addition and subtraction…

Q: -1 e -1 dt t 3x?

A:

Q: 4. dx (x² +1)*

A:

Q: ∫tan^3(x)⋅e^(tan(x))⋅sec^2(x)dx

A:

Q: e*dx е 2x+1 e

A:

Q: In the given equation/s as follows , find the indefinite integral:- See the equation as attached…

A: Given, 22I=∫1x9x2+1dx

Q: Solve the following indefinite integrals, using substitution or integration by parts where needed 10…

A:

Q: Evaluate the following indefinite integral. Use C for any constant of integration. da dæ x4/16x² –…

A: Given problem:-

Q: Evaluate the following integral as it is written. 1 4x 3xy dy dx 0 x3 1 4x 3xy dy dx = 0 x3…

A:

Q: Evaluate the definite integral given below. 7 dx 16+16x? Enter your answer in exact form.

A:

Q: For the indefinite integral V14+ x*dx, a good choice for a u-substitution is u = du = After making…

A:

Q: Evaluate the definite integral.

A:

Q: S dx х+2

A:

Q: Evaluate the following definite and indefinite integrals. V6 (a) da V3+1 (b) / da V3 – r2 (c) x* +x…

A:

Q: In the given equation as follows , use a table of integrals to find the indefinite integral:-   See…

A:

Q: Evaluate the following definite integral: / -3x(-2x² – 1)° dx Enter your answer as an exact fraction…

A:

Q: 4. For each of the following improper integrals, find the value of the integral or explain briefly…

A:

Q: Evaluate the following integrals using Integration of Algebraic and Rational Functions. 1. ∫ ?^2 −…

A: To evaluate: The integral ∫x2-3x+4dx. Formula used: Sum or difference rule of integration:…

Q: ~2 .4 x* +1 dx 1 J1

A:

Q: Recall that the constant term, C, cancels out when evaluating a definite integral and therefore, the…

A:

Q: Evaluate the following improper integral. Give an exact answer. 1. dx 2/3

A: Given that ∫051x23dx, we have to evaluate the following improper integral.

Q: Find the indefinite integrals, if possible, using the formulas and techniques.

A: Given, part a: ∫x-1 Now we use the substitution u=x-1 so dx=du ⇒u du We know that, ∫xadx=xa+1a+1,…

Q: 2. Evaluate each of the following integrals using the indicated technique (additional techniques may…

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) xp x(In x8)9 1 + C g10in (x…

A: Please see below.

Q: 2 dx 2 4 + x?

A:

Q: Evaluate the following integrals using the substitution method. Answer numbers 1-2. Show your…

A: NOTE: You have posted multiple questions, we have solved the first question for you, if there is a…

Q: Consider the indefinite integral /a Væ* – 4 dæ: . - This can be transformed into a basic integral by…

A:

Q: Find the exact value of the definite integral below, using the substitution u = x x (√6+√2) 1+x² -…

A:

Q: x2 + 8x + 13 dx (x + 4)2

A:

Q: Evaluate the following integrals using Integration of Exponential Functions. 12. dx 13. [ 2** dx

A:

Q: Evaluate the following indefinite integral, 1 (e&r VI – -)dx x2

A: Given integration is: ∫e2x-x-1x2dx To find the value of integration. ∫eaxdx=eaxa+c∫xndx=xn+1n+1+c,…

Q: So S(xy²) dxdy 4. 3

A:

Q: b) f6xæ**dx 4 cosht)dt

A: We have to find the integrals.

Q: 9. S (6eº+1)/½ eo 10. |(1 + 2x)³ dx

A: We can solve as follows

Q: -c) S dx d) Sdx 4+x2 4+x2

A: To evaluate (c)∫dx4+x2(d)∫x4+x2dx

Q: Explain why each of the following integrals is improper  integral -infinity to infinity  x2 e -x2 dx

A: Given Data The integral is ꭍ∞-∞ x²e x2 dx   When one of limit or both limit points of integration…

Q: 2. Find the following definite and indefinite integrals. Use Substitution when needed a) f…

A:

Q: 3. Evaluate the following definite integrals using a change of variables. а. sin(2x) dx b. xVx+1 dx…

A:

Q: [sin x dx

A:

Q: Evaluate the following integral by using Odd and Even Powers Method: y = [ cos³ (;x) dx

A:

Q: 3x Se 3x-e dx

A:

Q: Find the following indefinite integrals: 243 dr (a) 192 (b) S(V= - 2") dz

A: here we have to solve , a) ∫x2+3x3+9xdx b) ∫x53-2xdx

Q: 1. Evaluate the following integrals using appropriate methods and simplify your answers. e* dx (b)…

A: The integrals can be solved using the substitution method for ease of calculations. To simplify the…

Q: Find the indefinite integral using the substitution x = 4 sin(0). (Use C for the constant of…

A: To find the indefinite integral ∫116-x232dx

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.