3. Use integration by substitution to perform the indicated integrations x2 a. J dx xp. x2+1 cos (x) b. J+sin? (x) dx esin (x) dx C. S sec (x)

Q: Q5) Find the integration by using (by part method): Se3x sin X dX

A: We can solve this using part method

Q: Find: 1. integral  ∫cos(lnx)/x2 2. integral ∫x3√1 − 2x dx 3. the average valueof…

A: 1. integral  ∫cos(lnx)/x2 2. integral ∫x3√1 − 2x dx 3. the average valueof f(x)=2−6cos(0.09(x−π)) on…

Q: 1. Solve the following integral by using the Integration by Parts. (a) x sin x dx (b) e 2x sin 2x dx

A:

Q: 1 To evaluate the integral dx, we (x2 + 2x)3/2 sec 0 1 substitute

A:

Q: 1 Use the integration formula ax dx = ax + C to find 4* dx and simplify. In(

A:

Q: Q5) Find the integration by using (by part method): S e3X sin X dX

A:

Q: b) - Demonstrate the repeated use of integration by parts by proving the reduction formula п-1 S…

A:

Q: B) Use the techniques of integration to evaluate. (Solve 2 only) 3) J tan-ty dy dx 2) (1– x²)5

A:

Q: 6. Which of the following integrals cannot be evaluated using integration by parts? A. ſe-*sin2x dx…

A:

Q: 6) Use integration by parts to evaluate the following a) S Vx In x dx b) S e2x cos3x dx c) S“ x³ cos…

A:

Q: - x$ tn*(1+3x®) Using the appropriate integration formula to evaluate dx, the du = N. %3D 1+3x

A:

Q: Q: Find the integration for the following functions: - 1.- °(1-cos2x) 2-5 2- sin(tnx) dx 3-f-…

A: According to the guidelines issued by the company we are supposed to answer only first three sub…

Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: 3) (a) Use integration by parts to find the indefinite integrals of: e* sin 2x dx (b) Use parametric…

A:

Q: Q2. Use integration by parts method to evaluate the following integrals. 1. dx 2. S cos x? dx -dx 2…

A:

Q: Which of the following integrals is NOT appropriate for a substitution method? A 5x*sin(x³)dx ®…

A:

Q: 13. If u(x) = sin 3x and v(x) = x, what are du and dv? Writedown  u dv and  v du in this…

A: Given- ux=sin3x and vx=x To Find- The value of du and dv, write down the value of ∫udv and ∫vdu,…

Q: Solve f(x) Sin e* (4 nodes) Using Gaussian Integration (Numerical Methods) [ f(x) dx

A: Given function is f(x)=sinex We have to calculate ∫-11sin(ex)dx Formula for 4-point gauss quadrature…

Q: Establish the following integration formulas with the aid of residues: cos x - dx xt + 20x² + 64 `

A:

Q: 2. Integrate: Integration by Parts cos?x dx

A: Given : Integral cos2(x) dx

Q: Q1) use two method of numerical integration to approximate |x*cos(x?) dx n = 8

A:

Q: 1. Evaluate the integral 2 1-2 8x cos y dy dr y - 4 by reversing the order of integration.

A:

Q: J cos(2x)e2x dx (recurring)

A:

Q: Find the most general antiderivative (a) Integral [ (cos(ln x)) / x ] dx (b) Integral [ (x2)(ex^3)…

A: Given (a) ∫coslnxxdx  (b) ∫x2ex3dx  We have to find the most general antiderivative.

Q: !!! 6 cos (x2) Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Triple integral

Q: 9. Use integration by parts to show that pP+1 ]n°(x) |aP In°(x) dx p+1 p+1

A:

Q: Q1: Evaluate the following Integration: a) ( In(x²+x)-Inx-en3 dx b) S; sinx Ine(x+1) 1-cos²x

A: Answer (a): To evaluate this integral, apply the logarithmic properties : And, And, And, And,…

Q: 9. Determine the following antiderivatives: sec?(x) -dx- tan(x) 6. 4x (2x² + 3)°dx а. b. - sin(2x)…

A:

Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x*-1sin x…

A:

Q: dx Using the substitution x =2 sin 0 , evaluate the integral x²V4-x 2

A:

Q: Evaluate the following by changing the order of integration: 4 4 cos(y²) dy dx. 2.

A:

Q: Show detailed solution to the following using ti integration. x'dx 1. Integration by Parts J Vx4-5

A: Let's find.

Q: 5. The integration form of , XY dA where Dis the portion of x+Y = 2 in the 1" quadrant will be

A:

Q: Ql: Find the integration of : 1. S cos (3 sin x)cos (4 sin x). cosxdx

A:

Q: 02:- By using integration by part, find :- (Choose two only) 1- Sxe-* dx 3-S(1+ x²)e¬*dx 2-f Inx…

A: As per the company guideline's we are supposed to answer first question as mentioned by the…

Q: To integrate x3 ex2 x " 0x we apply integration by parts and in the form u dv, dv is set as:

A:

Q: evaluate using Integration by Parts.

A:

Q: Perform the following integration. 1. (sinhr) (coth² x + csch³ x) dx sec³ x tan x 2. S dx √2 + sec x…

A:

Q: Step 2 1 To find the integral S H x cos 8x dx by the parts formula, use u = x and v = Apply the rule…

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

Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Sx". .n-1 + n[x²- x" sin x dx = -x cos x + n cos x dx

A:

Q: We want to compute the integral tan e dx. If we use integration by parts, with u(x)=tan-lr and…

A:

Q: Consider evaluating x ln x dx using integration by parts. Which of the following would be the best…

A:

Q: A. Integration By Parts 1. ſx5Vx3 + 1 dx 2. S/* x sin 2x dx 3. S- x³ex? -dx (x2+1)2

A:

Q: 1. Perform the integration. Show all necessary solutions. 8t² + sin t sint + cos ty dt co t

A: Find your answer below

Q: 34. e4x cos 2x dx

A: Solution:Given∫ e4x cos 2x dxFormula:∫udv=uv-∫vdu∫sin ax dx=-cos axa+C∫cos ax dx=-sin axa+C∫eax…

Q: Q2// Suggest a suitable integration factor :for this DE مع کتابة كافة خطوات اختر الاجابة الصحيحة…

A:

Q: Evaluate using Integration by Parts. x sin(4 – x) dx (Use symbolic notation and fractions where…

A:

Q: Q.4 Use the integration by parts to evaluate the integral. V3 2 sin-1 x dx

A:

Q: 4 16–x² Change the order of integration. Do Not Evaluate. 5tan xy dy dx

A: Answer

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.