Sõlve the integral - In 3 x'e-*dx 2.

Q: Solve the integral shown below. . S | xsin xdx

A: Given problem:- ∫x sin(x)dx

Q: Determine if the improper integral converges or diverges: 1 dx. 1+x²

A: Our Aim is to determine whether the improper integral given below converges or diverges∫0∞11+x2 -(i)

Q: Find the indefinite integral. Solution in handwritten. 1. fx sin x² dx

A: Indefinite integral

Q: •2 dx

A:

Q: 2 3 dx

A: Some properties of integration  I=∫g'(x)f(g(x))dx, put  t=g(x)   then I=∫f(t)dt ∫axdx=axloga+C

Q: (x+2) dx /3-2x-x2

A: Integration:                             ∫(x+2)3-2x-x2 dx

Q: Solve the definite integral using usub

A: To integrate,

Q: Find the indefinite integral.

A:

Q: Find the indefinite integral ∫(5 + 4x2)2 dx

A:

Q: Find out if the improper integral converges or diverges. If the given converges, find its value.…

A: Solution

Q: Find the indefinite integral ∫ dx/√(1 − 4x2)

A: Consider the integral, ∫ dx/√(1 − 4x2) Let f(x) = 1/√(1-4x2) By using the trigonometric…

Q: Find the indefinite integral.

A:

Q: g integral. dx

A: Given query is to find the value of the integral.

Q: 2 x ln((2x)²) dx 1

A:

Q: - Determine the indefinite integral : In(x³) dx.

A:

Q: In x dx.

A:

Q: Find the indefinite integral.

A:

Q: Find the integral of sec^4 (3x) dx

A: Given: ∫sec43xdx

Q: cOs x In(sin x) dx

A: Given,  ∫cos x ln(sin x) dx

Q: Evaluate the integrals in ∫log10 x/x dx

A: Given integral is: ∫log(10x)xdx To evaluate this integral, first apply the logarithmic property…

Q: Evaluate the integrals that converge 32 1 dx 2 ㅇ x5

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3. Does the improper integral 2 dx converge? et +e-*

A:

Q: dx (apply the properties on how to solve improper integrals 1 – x²

A: Given query is to find the value of the integral.

Q: -1)*dx

A: Given  ∫02(x-1)2 dx

Q: solve the integral: I1= integral of 1/((x-1)(x2-4x+1)) dx

A:

Q: calculate the indefinite integral.

A: first, we separate the integral

Q: Solve the following Integral Equation by Method of Successive Approximation:

A: Given: y(x)=1+λ∫011-3xty(t)dt This is in the form g(x)=f(x)+λ∫K(x,t)g(t)dt In the method of…

Q: Find indefinite integral.

A: ∫5lnz+3z dz Put, 5lnz+3=t⇒5·1z+0=dtdz⇒1zdz=dt5

Q: Evaluate the indefinite integral. -dx 1 – x8

A: We use the standard integration result ∫11-x2dx=sin-1x+C

Q: √ √√x√1 - x-¹ dx

A: To find out the integration

Q: s/4 dx 2- 1+tanx 3.

A:

Q: Evaluate the integrals in ∫e-1/x2/x3 dx

A: ∫e-1x2x3 dx Put, -1x2=t⇒2x3=dtdx⇒1x3 dx=dt2

Q: Find the integral

A: To integrate ∫ln|4x+5|dx, use the substitution method and consider 4x+5 as t. Differentiate both…

Q: Evaluate the integrals that converge: 3 dx 2x ! b) | a) dx (x² + 5)³ 3 – x -00

A:

Q: Approximate the integral from 3 to -3 of (2+x2) dx using five equal subintervals.

A: We have to divide -3 to 3 into five equal subintervals.Length from -3 to 3 is 3 - (-3) =6So length…

Q: Solve the integral. x +1 -dx 4. 4 + x2

A: Our Aim is to integrate the expression given below:-∫x+1x2+4dx -(i)

Q: Find the indefinite integral 3x2 dx et 2.

A: ∫ex-3x22 dx

Q: Evaluate the indefinite integral -dx x4 + 3

A:

Q: Evaluate the integrals in ∫log2 x/x dx

A: Let the given integral be y - y = ∫log2xxdxy = ∫log2×xxdxy = ∫log(2)+logxxdx…

Q: Evaluate the integrals ∫ln (x - 5)/x - 5 dx

A: Consider the provided integral, ∫lnx-5x-5dx Evaluate the provided integral, Apply the u substitution…

Q: Evaluate the integrals in ∫ex/2 dx

A: To evaluate ∫ex2dx

Q: dx -> X-VX dx 12 X-(X) b.) =In (x-1x)?

A: Solve the given integral

Q: Evaluate the integral that converge dx (2x- 1)3

A:

Q: What is the integral of dx/(1_4x)

A:

Q: In -dx x²

A: This is a problem of integration. Based on the general formula of integral by parts we will solve…

Q: Find the indefinite integral. 8x In (5x)dx

A: The given indefinite integral is ∫8xln5xdx.

Q: In x dx

A: Given: ∫lnxx2dx Integrate the given integral using the integration by parts formula.

Q: Find the indefinite integral. ∫e3x+1 dx

A: The given integral is ∫e3x+1 dx

Q: Evaluate the integrals in ∫ln 2 log2 x/x dx

A: ∫ln (2) *log2xxdxChange of base rulelogab=logcblogca Formula∫xndx=xn+1n+1+C

Q: Find the indefinite integral. 14x In (3x)dx

A: From the given problem:   I=∫ 14xln3xdx=14·∫ xln3xdx   From the integration by parts:…

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.