31. An alternative derivation of the surface area formula Assume f is smooth on [a, b] and partition [a, b] in the usual way. In the kth subinterval [Xx-1, Xx], construct the tangent line to the curve at the midpoint m = (xg-1 + xx)/2, as in the accompany- ing figure. a. Show that Δx. n = f(m;) – f'(m;) and n = f(m;) + f'(m;). Δxε b. Show that the length Lỵ of the tangent line segment in the kth subinterval is Lį = V(Ax)² + (f"(m²) Ax4)². y = f(x) r2 х Xk-1 тe -Ax

Q: Q3/By using matab find the area under the curve f(z) = z cos(z) for -4 SZ<9.

A: The area under any curve f(x) bounded within the interval [a,b] is given by: Area=∫abf(x) dx

Q: Find the area bounded by the following curves.  x = 1/2, x = 1, y = 0, y = √ 1-x2/x

A: Given: The curves are

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A:

Q: 6. Let C be the positively oriented circle centered at the origin with radius Without evaluating the…

A: We will use the principal branch of logarithm

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A:

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Q: Use the substitution u = x to find the exact area bounded by the curve y x2 the x-axis and the line…

A:

Q: Evaluate the following integral using a change of variables. xy dA, where R is the region bounded by…

A:

Q: what is the sigma notation for the right-hand approximation of the area inder the curve f(t)=t^2…

A: Let's find.

Q: Suppose that  0 &lt; c &lt; pie /2 . For what value of c is thearea of the region enclosed by the…

A: Here the objective is to find the value of c.

Q: O What is the area enclosed betmeen the curves y=X dy= 6-x² on E2,37?oB

A:

Q: Find the area of the region bounded by the 7e 4 on the interval T <0 < 2r. given curve: r = IT <o<

A:

Q: Find the Area between the curve y = sin(x) and y = cos(x) and the lin es x = 0 %3D and x = n?

A:

Q: Find the area of the region bounded by the following curve. The limiçon r= 6-4 cos 0

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Q: Find the area of the surface formed by revolving the graph of f(x) = x3 on the interval [0, 1] about…

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Q: Find the area obtain when the curve f(x) = x² – In æ, for 1 < x < 3, is rotated about the y-axis.

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Q: The area bounded by the curve x = 3y + 8, the y- axis and the abscissas y = 0 and y = 2 is O 19 O 1…

A:

Q: Find the area bounded by the following curves : A] y = cos(x) + 1 , y = 2, and x = T B] y = sinh(x)…

A: The region is given by

Q: Which of the following corresponds to the total area bounded by the curve y= x - 3x² + 2x and by the…

A: The region bounded by the curve y=x3-3x2+2x and by the x-axis from x=-2 to x=2

Q: Find the area bounded by the parabolic arc Vx + Jy = 7 and the chord joining (9, 16) and (16,9).

A: Topic = Application of integration  Area = 7/3

Q: Find the area of the region bounded below by the curve y , to the left by the curve y = || cos(x)…

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Q: For any R>0, let CR(0) be the circle of radius R and center zero oriented in the counterclockwise…

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A:

Q: Compute the area between the following curves y = x° and y = -3x2 on the interval |0, 2|

A:

Q: Suppose that 0 <c <n/2. For what value of c is the area of the region enclosed by the curves y=cosx,…

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Q: Consider the following integral along the given positively oriented curve C: 1=[(1² -4x)dx+(2+x*y)v…

A:

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A: Approximation

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Q: Given that R is the region bounded by the curve y = x+3 and line y = x-3. (c) By using the limits in…

A:

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x y=0, x=TT/4, x= TT/2 ? ans/ 1/2

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Q: Evaluate the double integral / | y dA; R is the region in the first quad- R rant enclosed between…

A: O

Q: 2. Use the appropriate integral theorem (and state which one you are using) to evaluate Lr*y dr –…

A:

Q: Find the area of the of the region that bounded by the following cases: TT 1- the curve y = cosx…

A:

Q: Determine the area of the region between the following curves. (a) y = sin(x) and y = cos(x) on x =…

A: The given curves are y=sinx, y=cosx on x∈-3π4,9π4.

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A:

Q: f(x) = }x* + [1, V2]

A:

Q: Approximate the area under the curve of y = x² + 3 over the interval x = -3 to x = 1 using 4…

A: Recall: Trapezoidal rule  Area=∫abf(x)dx≈∆x2fx0+2fx1+2fx2+···+2fxn-1+fxn where, ∆x=b-a2 We have,…

Q: Find the approximate area under the curve of f (X) =cos ( from x =0 tox=T, Using 4 trapezoids. 3 2.6…

A:

Q: Find the area obtain when the curve f(x) = x² - In r, for 1 <a< 3, is rotated about the y-axis.

A: The area obtained when the f(x) is rotated about the y-axis is given as: where a is the lower limit…

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A:

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A:

Q: Find the area bounded by the line y=4 and the curve described parametrically by: x(t) =…

A: Given: y=4x(t)=t-1t,    y(t)=3t+1tSince y=4,  y(t)=3t+1t ⇒ 3t+1t=4⇒3t2-4t+1=0⇒3t2-3t-t+1=0…