1. Evaluate the indefinite integral (a) S (e2× +– 3) dx (b) S(4x³ + Vx)dx 2. Find the function f(x) if f'(x) = x-3 + 2, ƒ (1) = 3

Q: Find the integral of (e^x - 1)/(e^x + 1) dx.

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Q: Evaluate the integral: e³+cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 2In3 + C (3e)3+ sinh2x B 2 + In3…

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Q: 1. Find the following integrals. i) S 3e-2x dx 2x2-1 dx ii) S: 2x3-3х

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Q: 4. Evaluate the given integral. |(x + 1)(x – 3)| dx -2

A: Solution:Given∫-20(x+1)(x-3)dx =∫-20(x2-2x-3)dx= ∫-20(x2-2x-3)dx= x33-2x22-3x0-2=0--83-4+6=23

Q: 1. Find the definite integrals of the following functions : (a) L. 4.x dx (h) dx ex +1 -2 0. (b) /…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: 1) Find dy/dt for if : y = log2 (81n 2) 2) Evaluate the following integral= In 2 log2 (x + 2) dx x +…

A: Any logarithmic function having a base other than e can b converted to a natural log as shown below:…

Q: 1 Suppose we perform the substitution u=3+Vx in the integral dx . I (3+ Vx)4 What is the resulting…

A: we have to find the given integral

Q: d/dx integral from e to x^3 ln(t^2+1)?

A: If Fx=∫b(x)axf(t)dtthen dFxdx=ddx∫b(x)axf(t)dt=faxa'x-fbxb'x

Q: 3. Find the indefinite integrals. (a) /4 dx (b) /2* r 2x-x2 dx

A: Given two functions integrate it by use of formulae

Q: If you are asked to find the indefinite integral of f(x) = x ln(x), and you are told to integrate by…

A:

Q: Find the indefinite integral.

A: Let ex+e-x=v. Differentiate both sides: (ex-e-x)dx=dv Substitute v and dv in the integral…

Q: 1 Find the indefinite integral || e* + dx 1+x?

A:

Q: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

A: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

Q: Evaluate the integral. -^x dx e S² sin √1-x² 2

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Q: 1) Find dy/dt for if : y = log2 (8r'n 2) %3D 2) Evaluate the following integral: In 2 ` log2 (x +…

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Q: S dx 2.

A:

Q: 2x² +10x+9 dx = ? x.(x+3) integralinin eşiti aşağıdakilerden hangisidir? X B) In x+3 A) In(x² +3x)…

A: Consider F(x) = 2x2+10x+9x(x+3)2 We will solve it by partial fraction Let Ax+3+B(x+3)2+Cx =…

Q: Find the integral of (1 2x) e^ (-x) dx from x-0 to x=. с. 2 А. 3 в. 4 D. 1 O B

A: ∫ uv dx = u ∫ v dx - ∫ (u' ∫ v dx) dx. ∫ (1+2x)e-xdx = -(1+2x)e-x + ∫2e-xdx ∫ (1+2x)e-xdx =…

Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

A:

Q: How do I find K of the integral e^(x^2/2)dx on the bounds from 0-2 what is E_T? and what must n…

A: Given: The error in trapezoidal rule is given as:

Q: e*dx e -x +1

A:

Q: Find the following indefinite integrals subject to the initial conditions a) y'= with y(1)=0 x²+6'

A: topic - differential equations

Q: Evaluate the integral of sin^6 x dx from 0 to T/2.

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Q: 1. Evaluate the integral of x2 (3 - 2x) dx if upper limit = 2 and lower limit = -1. а. 12 b. -12 C.…

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Q: Evaluate the improper integral e-1/x dx

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Q: Find the indicated integral (if it exists) / e bx dx e12z +1

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Q: d'y Find the particular integral solution of dx - =x+3cosx+e". dx

A: I am using the formula for constant coefficient

Q: Solve the Indefinite Integral. xe²t S dx (2x+1)² A [1-21] +0 e2x 2x C 4 2x+1 B. 2-2(22+1) + C 4 C.…

A: SOLUTION-

Q: 2. Find the indefinite integral (Scos(4x) + √x dx

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Q: 5 Find the following indefinite integrals. 10 b. J- S(x+2)' dx a. (3x-7) xp-

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Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: Q3: Find the integral for the following functions: - 1) 2 6 dx 2 x+2 2) S 3co t(x). csc²(x) dx 3)…

A: To find the given integral.

Q: 5. Find the indefinite integral. A) f dx (x-3)Vx -6x+5

A:

Q: Can i get help step by step with this problem?

A: Given:

Q: 1. Evaluate the given integral Q. √x²+1 (x - y² + 1) dy dx

A:

Q: 11:32 E O 1 Evaluating the integral f In(x)dx, where x> 0 yields:

A:

Q: 39.: * Compute the integral: x (Inx) dx. a. (5e –1) b. (3e -1) c. (e +2) d. (5e -e') (e* -e) 32 16…

A: Use by parts integration

Q: e2x 2.) S. dx ex – 5

A:

Q: -2 Evaluate the definite integral S: 1 dx. 1 x+a²

A: general answer is Ln|(2+a^2)÷(1+a^2)| Where a = -3/5 Final answer is Ln|59/34|

Q: 4. Determine the following indefinite integrals: a) S(2x + 3x -7x2 + x-5) dx %3| b) S(x – 5)² dx g)…

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Q: Q4. Find the integral of the following functions x dx (x-1)(x2+2x+1)

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Q: Evaluate the integral: x² e3a dx

A: This question is related to Indefinite Integral, we will use Integration by parts formula to solve…

Q: evaluate the given integral.

A: The given integral ∫2x+1xx2+4dx can be evaluated as, ∫2x+1xx2+4dx=∫2x2+4dx+∫1xx2+4dx The integral…

Q: Find the indefinite integral x2e +e² dx.

A: The given indefinite integral is: I=∫x2e+ex dx

Q: Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+cosh2x B 2ln3…

A:

Q: 3 Suppose that f(x) dx = 7, | f(x) dx = 5, and | f(x) dx = 10. %3D Evaluate the following definite…

A: (a) The given integral is: I=∫35f(x)dx As we know from the integral theorem,…

Q: The definite integral from 0 to = of cos x sin xesin² x dx is 4 O e - 1 e+1 e-1

A:

Q: Find the integral [(x** +(-1)°x*!) In((a+2)x)dx b+1 с+1

A: The integral has been solved n attached in the second step.

Q: Find a particular integral for d^2y/dx^2+dy/dx= sin x

A:

Q: Q3: Find the integral for the following functions: - -6 dx 1) L 2 x+2 2) S 3co t(x). csc²(x) dx 3)…

A:

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.