Write the algebrair exorasion as a trigoametric Function ot e where 06oc t/2. 18) x²-16, x= 4 seco

Q: G> As Dng Evaluate the Hollow 2. Sinh 5zdz zcos2zdz SHOT ON REDMI Y3 AI DUAL CAMERA

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Q: Express the limit as a definite integral on the given interval. COS X¡ lim Дх, [Зл, 5л] Xi i = 1 dx…

A: This question is related to definite integration, we will solve it using given information.

Q: let f(x)= cos(x)-sin(x)/ h(x)ex, what is f'(x)?

A: Find f'(x) fit given f(x)

Q: Use FTC I to show that x" dx = 0 if n is an odd whole number. %3D Explain graphically.

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Q: 7. S(2 + tanx)²dx

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Q: Find the area bounded by the trigonometric curves y=sinx and y=cosx from; x== 3.459 square units…

A: Area bounded by the curve .

Q: Express (3*) dx as the limit of a sum. 1

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Q: Now, approximate the integral 3 r(x)dx by using a left-hand sum with 3 rectangles of equal widths.…

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Q: Find the intervals where the function f(x) = 2cosx + 1/ sin2x, 0≤x≤ 2π is concave up.

A: Let's solve.

Q: Find the intervals where the function 1 f(x) = 2cosx + sin2x, 0 ≤ x ≤ 2π is concave up.

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Q: Evaluate f tan²xsec*xdx using trigonometric integrals

A: Our Aim is to evaluate the integral given below:-∫tan2 (x) sec4 (x) dx -(i)

Q: Çind in fefinite intregal s .2dx - 2x+1 %3D

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Q: Use all your background to find the integral of the hyperbolic function: 00 sinh ax cosh bx

A: Given: The given integral ∫0∞xnsinhaxcoshbxdx

Q: 3 dx by Simpson's rule breaking it into 6 intervals. Evaluate 2+x?

A: We have to evaluate the integral ∫2532+x2dx by Simpson's rule-breaking it into 6 intervals.

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. 9+x…

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Q: Q. Use first principle rule and proue that if y=s %3D secl tand = secx

A: Given: y=secx We know that for any given functiony=fx, first derivative is given by…

Q: How do you use a Maclaurin serieis aproximation to estimate (Provided picture). Thanks!

A: First find the Maclaurin series for e^(x^2) using the Maclaurin series of e^xPlug x^2 in place of x.

Q: . Suppose a certain object moves in a straight line with the follov eters per second and / is in…

A: we have ,  v(t)=-2+t+3 sin(πt) .............(1)

Q: Use the midpoint rule with = 2 to estimate 1 dx. Hint Ax = 2 m1 = and m2 = Answer 24 35

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Q: Lim sinx? s 2x Cos COS X

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Q: 1. Use the trapezoidal rule with eight intervals to evaluate places. I = [dx 3 2 %3D correct to 3…

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Q: Find f'(x) given トhat fcx)= tan Cax - Jx +4ょ3) %3D (assume real number) is

A: Our aim is to find f'(x) where f(x)= tan(ax5-x12+4x-3), where a isassumed to be a real number.

Q: Use geometry to evaluate f(2x+5)dx

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Q: use the gaussian quadrature formuld to estimate it cund onilt foddxit, where fad =x+2

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Q: Use the trapezoidal rule with n = 5 to approximate cos(x) -dr Keep at least 2 decimal places…

A: The trapezoid rule is

Q: How many periods of the function y = tan x are there between -27T and T? %3D [?]

A: We have to find

Q: A. Evaluate. 1 (sinhx - sinhx +coshx cosh?x 1. dx

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Q: When observations are mea than counted, continuous da the outcome. Soloot on

A: Yes, so many times we measured the observation rather than counted. For example, we measure height,…

Q: aln(Vx) dx

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Q: Find anti deriva tive Fa) of the function, an foal- fxl = 5 sinx such that Flo) = 8+ cosX

A: Now,

Q: Approximate sinx dx using four trapezoids of equal width. On the interval (0, pi)

A: Trapezoidal rule

Q: Q3/ By using definition, proof that cot x = dx csc2 x.

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Q: tan' (x) sec (x) dæ

A: We have to evaluate the indefinite integral.

Q: The process followed by a variable x is: dx = function f(x,t) = In(x/t)? uxdt + oxdz.What is the…

A: Given:     Using x is : dx=μxdt+σxdz find the process for the function f(x,t)=In(xt).    Also that…

Q: Use the trapezoidal rule with n = 8 to approximate %3D cos(x) Keep at least 2 decimal places…

A: We have to find the value of the integral∫16cosxxdx using trapezoidal rule with n=8. From…

Q: lim (x+sin(÷)

A: Let, L=limx→∞x+sin1x1x...(1) So, the form the expression is ∞0.

Q: Sa J (1+ In² sin x)5 “ cot x In sin x dx

A: Let the given integral be y - y = ∫cotx lnsinx1+ln2sinx5 dx           ..............(1)Let,u =…

Q: x* sec x tan x du

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Q: Let f(x) = sinh x, where sinh x = %3D Find f"(x).

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Q: Approximate the sol of x = sinx upto 4 decimal places by using Newtons method.

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: Given query is to find the interval where graph concave up and down.

Q: find f'(x), where f()=Dcosx sin x.

A: The given function is, f(x)=cosxsinx. Obtain the derivative of the given function using limit…

Q: Sinx +x 3) lim tan x

A: Given limit is : limx→0sinx+xtanx Use property of limit  limx→0sinxx=1limx→0tanxx=1

Q: (i) By making the substitution o = tan 0, demonstrate the validity of %3D Parseval's theorem for…

A: Consider the function as ft=e-tdt

Q: ind the regions where sinx Sx.f

A: Given that sinx ≤ x. The obejctive is to find the region that satisfies the given condition.

Q: Differentiate each of the f cosh(x)+1 cos(r)+1 a. Y =

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Q: b.

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.