Evaluate ∫x3 √(1 - x2) dx using integration by parts.

Q: Evaluate the integral. 4 dx Vx (1 +4x) X,

A:

Q: Evaluate the integral dx x"+ 4

A:

Q: Evaluate the integral. (Use C for the constant of integration.) dx 81 - x2

A:

Q: Evaluate f 5z" In8x dz using integration by parts.

A: Given integration: ∫5x7 ln8x dx Use the integration by parts: ∫u v dx=u∫v dx-∫dudx∫v dx dx Here…

Q: Use the basic integration rules to find or evaluate the integral ∫x2 √(x3 − 27) dx

A: Now put

Q: Evaluate the integral. (Use C for the constant of integration.) x2 dx 49 – x2

A: With the help of trigonometric substitution we can easily solve this question. Try putting x=7sin(t)…

Q: 1 dx X+4

A:

Q: Use the substitution formula to evaluate the integral. 4 8 - Vx 15) S" dx 1

A: Let's find the value of indefinite integral first: I=∫8-xxdx Substitute 8-x=u⇒-12xdx=du⇒1xdx=-2du…

Q: dx XV 16x4 – 1

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x² dx 81 - x2

A: Given,             ∫x281 - x2dx

Q: Evaluate the integral. (Use C for the constant of integration.) x² + 9x + 1 dx (x² + 1)2

A: Make two parts of the integration.

Q: Evaluate the integral. (Use C for the constant of integration.) 10e-0.7x dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 6 dx 2x + xVx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 49 dx .3

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 7x2 + x + 7 dx (x² + 1)2

A: The given integral is: ∫7x2+x+7x2+12dx To evaluate the given integral.

Q: Evaluate with the order of integration reversed..... 4 11: x dx dy

A:

Q: 1. fx³ In x dx

A: Evaluate the integral equation by integration by parts .

Q: Evaluate the integral. (Use C for the constant of integration.) x2 + 7x + 1 dx (x2 + 1)2

A:

Q: 1 dx x² – 4x + 4

A:

Q: Evaluate the integral. (Use C for the constant of integration.) + 5x2 + 6x + 5 dx + (x²+ 1)(x2 + 6)

A: Use linear factorizing method and solve the integration.

Q: Verify the power rule for integration fx'dx= n+1

A: Given a power rule of integration,

Q: Evaluate the integral. (Use C for the constant of integration.) | (3x5 - x4 + 1) dx

A: The objective is to evaluate the integrals

Q: Evaluate the integral. (Use C for the constant of integration.) (x6 − 6x2)4(x5 − 2x) dx

A: From the given problem:   I=∫x6− 6x24x5 − 2x dx...(1)   First simplifying:…

Q: Find the integral. (Use C for the constant of integration.) (x8 + 9-X) dx

A:

Q: xe dx

A:

Q: Efxe*dx (1+x)2

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x2 - 49 dx

A: Find your answer below

Q: Evaluate the integral. (Use C for the constant of integration.) x + 21 dx x + 20x + 104

A: Consider the provided integral, ∫x+21x2+20x+104dx Evaluate the provided integral. Apply the…

Q: Use integration by parts to prove the reductionformula.

A: We have to prove the reduction formula using integration by parts method: ∫xnexdx=xnex-n∫xn-1exdx If…

Q: Evaluate the integral. (Use C for the constant of integration.) 9x dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x2 dx 25 – x2

A: Let, Integrate using substitution,

Q: evaluate the integral

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 3e3x dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 9xV1- x4 dx

A: Formula used: ∫a2-x2dx=xa2-x22+a22sin-1xa+C Calculation: Simplify the integral as follows:…

Q: Evaluate the integral. (Use C for the constant of integration.) X + 14 dx + 2x + 5

A: Topic - integration

Q: Evaluate the following using an appropriate technique of integration. (b) (5 – x2)³ dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 17xe2x dx (1 + 2x)?

A:

Q: O Integrate In 2x dx by using integration by part.

A:

Q: What is the result of the following ? integration dx Vx 4

A:

Q: Calculate the integral. (Use C for the constant of integration.) dx XV 36x4 – 1

A: Given, ∫dxx36x4-1 We have to evaluate the integral.

Q: Evaluate the integral. (Use C for the constant of integration.) dx 3 - 3x9

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 36 dx v3

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (2x4 – 4x-2 + 3x + 4) dx

A:

Q: Use the basic integration rules to find or evaluate the integral ∫x/ 3√(4 − x2) dx

A: The given integral is ∫x4-x23dx.

Q: a) Evaluate 1| dx by using integration by parts.

A: Dear learner, as per our guidelines we can provide the solution for first one only. Kindly post…

Q: Evaluate the integral. ( Use C for the constant of integration. )

A: The given integral is ∫x+21x2+20x+104dx. Evaluate as follows.

Q: Evaluate the integral. (Use C for the constant of integration.) dx 49 - x2

A: We have to find the integral

Q: Evaluate the integral. (Use C for the constant of integration.) 13 dx xV 9x2 - 1

A:

Q: Use the basic integration rules to find or evaluate the integral

A:

Q: 16 dx Vx-1 6,

A: I=∫9161x-1dxPut u=x-1differentiate w.r.t.xdu=12xdx2xdu=dx2(u+1)du=dxas x→9  ,u→2 as x→16 ,…

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.