49-52 Sketch the curve and find the total area between the curve and the given interval on the x-axis. 49. y=x²-x; [0,2] 50. y sinx; [0, 3π/2]

Q: b. The region R enclosed by the curves y = x and y = x² is rotated about the x-axis. Find the volume…

A: Given that region is bounded by the curve y=x and y=x2first find the intersetion point of the curves…

Q: Using integration by parts, Then k is? (a)-1.5136 [²x³ cos(x²) dx = k - [*²x sin(x²) dx (b)-1.1365…

A: Our Aim is to find the value of k by evaluating the integral using integrationby parts.∫02 x3 cos…

Q: Consider using the method of partial fractions to solve x²+x+1 Sa 2x²+2+x²+x A In(x²+1) B x+2 D…

A: This is a problem related to integration of the function using partial fraction decomposition. Based…

Q: Consider using the method of partial fractions to solve dx x²+x+1 2x²+2+x³+x - dx = [Aƒ (x) − B…

A: Given problem:-

Q: Using trigonometric substitution, what is A 1 6 sec-¹ (37) + √x²-9 2x² +C Ⓒ 3 sec ¹1( 3 ) + √x²³ - 9…

A:

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = − 1 − 2x, dv = f(x)dx, then the…

A:

Q: (A) = and B D = . Find the vector projection of A onto 2AD- BO O O O none of the above

A:

Q: 10. Given the following contour map: (Explain your answers) a) Is the surface a mountain or a…

A: 1 here is centre side (inside ) the contour level is increase so this is contour of mountain.   2 P…

Q: Question 16 A line through (-1, -2) with a slope of -10 has a y-intercept at

A:

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 6 in.…

A: A box with a square base and no top is to be made from a square piece of cardboard by cutting 6 in.…

Q: Write 20 terms of the Fibonacci sequence

A:

Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

A:

Q: √x²+a² =dx = _ (x²+a²)² 3a²x³ +c

A:

Q: 59-62 Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d evi dt sin sin…

A:

Q: Sketch a graph of f(x)=(x-2)² +4 6.

A:

Q: F(x) = integrate (3t + 2) dt from 2 to x + 2.  Use  first fundamental theorem of calculus to find…

A:

Q: Find I see sec42x tan 92 dx

A: The objective of the question is evaluate the indefinite integral.

Q: 12 || ti + t²j||dt = |

A:

Q: Explain why you think the series Σ01 77 converges to a finite number (-8)"-1 or diverges. If the…

A:

Q: mby f(x) = (lnx) (sin x). The figure above

A:

Q: Use the formula к(t) : = ||r′(t) × r"(t)|| ||r' (t)||³ 9t r(t) = e⁹ti + e-tj to find k(t).

A:

Q: Consider the integral f sin-¹x dx. If we let u = sin ¹x and dv = dx, the integral can be written as…

A: The given integral,  ∫sin-1x dx

Q: 1. f (5x¹8x³ 2. f (4x + 2) de +6x² - 4x + 7) dx

A: Topic:- integration

Q: Given: (1+2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = f(x)dx, then the value…

A: Let's find.

Q: x³+x A. -1 dx = f(+ g(x)) dx, then A+ B. -1 + In(5/2) C. 1 dx, then A + f²g(x) dx is equal to D. -1…

A:

Q: Write an equation for a rational function with: Vertical asymptotes at x = 5 and x = -2 x-intercepts…

A:

Q: Y sinh(1) (use logarithmic differentiation) 3 (sec x)²/2[/cot-¹x]

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t² +4 1 lim = (?, ?) t→+∞0 8t² +9¹ 5t

A:

Q: 14. Evaluate the following √x-²sec (+)tan ³ ( =) « dx 2tan (²) [7tan² ( ² ) +11] +C 77 2tan…

A: To evaluate: I=∫x-2sec41xtan521xdx Substitute 1x=t⇒-1x2dx=dt⇒x-2=-dt So, I=∫sec4t  tan52t…

Q: π/4 x³ dx (x²+4)5/2 ST/4 (Use trigonometric substitution)

A:

Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

Q: 1. Three-digit numbers (a) How many repeating three-digit numbers can be formed using the numbers…

A:

Q: Given f(x)=√x-5;x#5 and g(x)=x+3. Find the domain of (gof)(x)?

A:

Q: C. y = 5x² + 2, x=0, x=2, y = 0

A:

Q: b) Determine whether the series n=1 find its sum. Show All Your Work! n-1 (-3)* 4" is convergent or…

A: We need to determine convergence.

Q: Find an equation of the plane containing the point (3,0,-4) and perpendicular to the line r(t)=…

A: A detailed solution is given below

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

A:

Q: x²+x+1 Sa 2x²+2+x³+x² (A (B (D) -b dx dx = [Aƒ (x) – B ln(g(x)]å + D ſb da , and if A = ‚B < 0, then…

A:

Q: graph each function using transformations or the method of key points. Be sure to label key points…

A:

Q: Describe the long run behavior of f(t) = As too, f(t) → ? v As t→→∞o, f(t)→→ ? - 4tº + 2t6-3t5+1

A:

Q: 8 An acceleration function is expressed as a (s, v) = s²- determine displacement by integrating '…

A:

Q: rπ/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

A: To evaluate the given definite integral.

Q: A B C The IBP formula fudv=uv-fvdu can also be written as f udv + ſ vdu : = UV Which of the…

A:

Q: dx If S = is solved by trigonometric substitution, which of the following x² - 2x - 4 substitutions…

A:

Q: 19. TT/2 -π/2 sin 0 de 20. * sec² 0 de

A: 19 ∫-π/2π/2 sinθdθ [-cosθ ]-π/2π/2 0 - 0 =0 other way sin is odd function so also integration is = 0…

Q: The demand for a product is given by D(x) = 150e-0.025x, where x is the number of units sold each…

A: Let's find.

Q: The height y (in feet) of a ball thrown by a child is 1 y 162² +42 +5 where a is the horizontal…

A:

Q: Question 13 > Determine the number and type of solutions for the equation 3x² + 30x+75-0 O Two…

A:

Q: Given: S√-x² + 4x+5 dx. Using trigonometric substitution, what is the integral form in terms of ? 9…

A:

Q: Question 7 Consider the Quadratic function f(x) = 9x² 4. Its vertex is ( Its largest z-intercept is…

A: