x dx J 7x2 + 3)5 (7>

Q: Vr² +1 dx = = -xVx* + l (8) +1 +-In x + +1+C

A: It is integration problem.

Q: 3. Evaluate J (2x + 5)(x + 5x)'dx.

A: The given integral is ∫2x+5x2+5x7dx

Q: dx 3+ Vx+2 x +

A: Here we solve the given problem of integration.

Q: dx Integrate: S x²-3x+2

A:

Q: Prove : (x2 + 2x + 2 )dx > 0

A: The given integral is ∫-10x2+2x+2-x2dx The integral has been rewritten∫-10x2+2x+12x2dx Apply…

Q: iate ſ In(x + v1 +x²)dx

A:

Q: ntegrate by parts f(x)=(x+1)2ln(3x) dx

A:

Q: 5. f(x)=xe" , find fInx. f'(x)dx .

A:

Q: T (3 sec² x + 4 csc² x) dx 3

A: The given integral,        ∫π3π43sec2x+4csc2xdx

Q: 4. f Inv9 - x2 dx - integration by parts

A:

Q: X √2x²-4x-7 S dx

A: Solution…

Q: [2 2x³ (x² − 1)² – dx|

A:

Q: Sla 1 z dx |(25 – x²)3/2]

A:

Q: Use integratiðn by parts lU Sxe*dx b. Sx sec2 (5x) dx C. SxVx + 1dx a.

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: Integrate by substitution. 2 [x²(x³ +5) dx

A: Given query is to find the integral using substitution.

Q: Use C for any constant of integration. ' 6x³ + 2x? – 20x – 12 - - dx = x² – 4 -

A: The given integral is ∫6x3+2x2-20x-12x2-4dx. We have to evaluate the given Integral

Q: Suppose that f(x) dx = 2. Calculate (5f(x) + 4) dx-

A:

Q: n/3 sec23x 8. n/4 2+4tan 3x dx

A:

Q: s x3 √1-x² V dx

A: Given: I=∫x31-x2dx   ...1   As we know that; The Power rule; ∫xndx=xn+1n+1+C

Q: = vt – 2. a²y y = t2 – 3' dx²

A: The solution are next step

Q: 1 dx 5 (V² -9) x² – 9

A:

Q: 1. dx x-19-x

A: Given :∫dxx49-x2

Q: 4 – 2x dx. x3 + 2x2

A:

Q: 4- x²+4 dx ht. 23

A: To evaluate∫x3x2+4dx We can find the integral by substitution method.

Q: Differentiate the function. (2x+5) y= (5x+1) 3 기 dx 11

A: Given:       y=2x+545x+13 differentiating with respect to x Apply the quotient rule:…

Q: uate the integral. 9. (x2 + 2x – 5) dx 4.

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

Q: 3x dx V1-x

A: Integral is given

Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: 3r² + 10x + 7) In (z²+3) dz

A: I am attaching image so that you understand each and every step.

Q: Integrate the function. 2 + 16 dx 2x2

A:

Q: Evaluate 2х— 7 -dx J x2 — бх + 10

A:

Q: Use n = 6 subdivisions to approximate the value of Vx +2 dx by the trapezoidal rule.

A: The given integral is ∫06x+2dx and the value of n is 6. Using the trapezoidal rule, approximate the…

Q: What are all values ofk for which x'dx = 0?

A:

Q: Evaluate integral 6x²–2x−1_dx b. S 4x -x

A: To evaluate the following integral. ∫6x2-2x-14x3-x dx

Q: 9. dx J1 (3x²+1)3

A:

Q: b. Find S 5x*(x5 – 1)dx using a suitable substitution.

A:

Q: 41Stañdx= Q22x+1 X'+2X+1

A: (1) Given integral is ∫tan−1xdx It can be written as ∫tan−1x⋅1dx Use integration formula…

Q: A) Evaluate 1 dx. I vit 6x – x² -

A: In this question we will use basic of calculus i.e concept of integration. First we will convert the…

Q: 14 Approximate (x2 - 3) dx using 4 rectangles. 2

A: Solution -    Given Integral is -  y=∫214(x2-3)dx    Now we have to evaluate the value of the…

Q: 4 dx Зx/10In(3x)- (In(3x))2

A: Given integral  ∫43x10ln(3x) -(ln(3x))2dx

Q: x²+2 dx x+2

A: We can solve the integral as below.

Q: Integrate ing with res pect to x; +8 - (3x+2) - the followi Sin (x) + + 2 4x dx 4 5x

A: Formula : 1. ∫xndx=xn+1n+1, n≠12.∫(ax+b)ndx=(ax+b)n+1a(n+1)3.∫1xdx=lnx4.∫sinx…

Q: | x(x – 2) sech(2x²e¬x) dx ex

A: To find: ∫xx-2sech2x2e-xexdx

Q: Evaluate and simplify. L dx 1 V1-2x-x²

A:

Q: B4. Evaluate the integral [(3x² - ª ++5 x -6) 4 +5 /x – 6) dx .

A:

Q: Use the Midpoint Rule with n = 8 to approximate 5.5 x°dx. 2.5

A:

Q: 3. (a) Determine 3 + x2 VI dx x2 (b) Determine 4 dx + x2

A:

Q: 4x2-3 f (x) 2х3+x2+7

A:

Q: Find if y=tanVx³). dx 1 A 1+x³ 1 (в 2/x³ (1+ x³) 3x2 (1 + x³) D 2(1+ x³)

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

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.