Compute / / sin(x²) !! dr dy.

Q: Find the integral. er sin(5x)dx - IT

A: Known integral formula:

Q: sin° (3x) cos“ (3x)dx 4

A: The given integral is ∫sin53xcos43xdx.

Q: .find integrals by using Beta fun dx (1-x*) ーズ

A: Using the Beta function, it can be written as follows.

Q: sin(x) + 1+x20 dr

A:

Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x +…

A:

Q: Use Newton Raphson method to obtain a root to 3 decimal places 1.   x^3-5x+3=0 2.   sinx=1-x

A:

Q: Evaluate the fsinz integrais belovo sin² xcsc 2x dx

A: Evaluate the integral

Q: To evaluate the integral |(2x+1)tan Vx dx using Integration by Parts, we should choose

A:

Q: Find the slope of the tangent line to the curve: 3.) Ħan0 at 0=n/4 4.) sin20 at 0=x/3 5.) rcos20 at…

A: Use the formula for the slope in case of polar coordinate.

Q: use the Mean value Theorem to establish Isine-siny </2-y) Ve,yER

A: We will prove the inequality as following.

Q: a) Differentiate f(x) = sin x from first principtes. %3D

A:

Q: Only one of these calculations is correct to evaluate the definite integral V sinx dx Using the…

A:

Q: Siny+ tany siny %3D 1+ secy

A: Let's find.

Q: [ cos² 2x sin² 2x dx

A:

Q: Find the indefinite integral ∫cosh2 (x − 1) sinh(x − 1) dx

A:

Q: Find the indefinite integral. sin(9x) sin(2x) dx (Hint: See the hint for Exercise 50 in Section…

A:

Q: Use linear approximations to estimate the following. 1. sin 9/4

A:

Q: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

A:

Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: */16 etan(1r) sec2(4x) dr

A:

Q: is 4= Sinh(2sinhix) shaw Hh at %3D 2 (a)

A:

Q: Use Simpson's rule with n = 4 to approximate 3 cos(x)

A:

Q: Evaluate the double integral [ Vy sin ydydx.

A: • Here, the inner integral w.r.t 'y' is difficult to evaluate, hence we have to change the order of…

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: sin x + 10(csc x)² dx

A: To compute: ∫(sin x+10(csc x)2)dx

Q: Evaluate the definite integral. ∫(lower bound=π/4)(upper bound=0)sin(4t)dt

A: Given,             ∫π40sin4tdt

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: This is exercise 12 of Section 7.5 page 460. Find the integral sin(2x) dx +C 1+ sin (x)

A:

Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Differentiate f at x = 0.5 using 5 point formula. Also…

A:

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

A:

Q: 4. Use Trigonometric substitution method to evaluate the integral: dx

A:

Q: Find the indicated midpoint rule approximation to the following integral. .3 2 sin 7x 2 x dx using n…

A: Calculate the delta x and the f(xi) for the given integral.

Q: 2) sin9xcos10xdx 3) sin xcos xdx XCOS dx 4) S

A:

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: sin 1+V dz

A:

Q: S sin4xVcos4x + 1dx

A: Let u=cos(4x)+1 Then du=(cos(4x)+1)′dx=−4sin(4x)dx  and we have that sin(4x)dx=−du4

Q: 2* csch (2*) cosh(2*)-sinh(2*)

A:

Q: calculate the integral.

A: Given integral is We will use the following substitution to evaluate the integral

Q: What is the integrable form of sin-cos-sino do?

A:

Q: Find the smallest positive root by using the bisection method S(x) = 4 cos(2x) – x' +5 with 3…

A: The smallest positive root by using Bisection method of f(x)= 4cos(2x) -x3 +5  is   1.2334.…

Q: What is the integrable form of sin-cos-sin0 do 2 2

A:

Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: The actual error of the approximation of I = x² sin (x³) dx using composite Simpson's rule with n=4…

A:

Q: b) By using integration parts, show that ii. S(3x + 5) sin(2x + 3)dx = -÷(3x + 5) cos(2x +3) +sin(2x…

A: By using integration by parts, show that∫3x+5 sin2x+3 dx=-123x+5 cos2x+3+34 sin2x+3+C

Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: The area under one arch of y=sin(0.5x) is O 0.2 O 0.5 O 0.8 None of them

A: Given: y=sin(0.5x)

Q: Find when 4= SINX Thuen dy (sinx) (ar f(s wheve for 0<x< M2 tanx taux a=?

A:

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.