Noting the range of the integral, compute .2 Jo (2² + 9)2dx.

Q: The area bounded by the curve y -V4 – x² and the x-axis over the interval -2, 2] is Select one: a. 4…

A: Realize that the given curve is the bottom half of the circle x2 + y2 = 4 i.e. bottom half of the…

Q: 2x2+4x+4 Estimate the area of the curve y = 2 from x = 1 to x = 3 by using 5 rectangles and right…

A: We find out the area of given curve usin Rieman sum where dalX=(b-a)/n where n is the number of…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 6. - dx (2 —…

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Q: Evaluate the integral. NOTE: Enter the exact answer. + 13/x| dx +C [ 20:r3

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Q: 1.S(2 + Vx)³ Vxdx

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x²e-9r³ dx +C

A: ∫x3e-x3dx

Q: a. Find the area below f(x) = -x² + 4x + 3 and above g(x) = -x³ + 7x2 – 10x + 5 over the interval 1…

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Q: b.) 3 dx 5/3

A: We will use substitution method.

Q: Q4. Approximate the value of f xv2x² + 1dx using the trapezoidal rule with n = 6. Compare this…

A: I am attaching image so that you understand each and every step.

Q: 2) Find the area bounded by the curve y=x² + x + 4, the x-axis and the lines x = 1 and x = 3. (Draw…

A: Given information: The curve given is y=x2+x+4, x-axis and the lines x=1 and x=3. The area of our…

Q: a. ²₁ (5x¹-2x³) dx

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Q: The area bounded by the line y = x, the x - axis, the ordinates x =1, x = 2 is 3/2 O 5/2 O 1/2 7/2

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Q: V5 - 4x — х2 dx

A: Used substitution to solve the integral.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x²e dx +C

A: The solution of the problem is given in the next step.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. dx (7x4 + 6)…

A: Given: ∫x37x4+63dxSubstitute  u=7x4+6       Then dudx=28x3…

Q: The area of the region bounded by y = v9– x² , the x-axis and the line first quadrant is: O 9(n+2)/8…

A: Given: To explain the correct option of the given statement as follos,

Q: The area bounded by the line y=x, the x − axis, the ordinates x =1, x =2 is ___ O 3/2 sq units O 5/2…

A: area

Q: 2. Find the area bounded by y = 2x? + 10 and y (Hint: you will need both points of intersection). =…

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Q: Find the area of the region bounded by the line y=(1/2)x and the parabola y? = 8-x.

A: Area between curves

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (7x – 6)° dx…

A: To evaluate the integral ∫7x-69dxFormula:∫xkdx=xk+1k+1+C

Q: Use the graph to find the values of the integrals, given that f(x)dx=4. -2 ,2 f(x)dx = f(x)dx = -2…

A: We know that Integral is the area sum of the region above x axis minus area of the region below x…

Q: Evaluate the integral. f32 d= -2 dx +C %3D NOTE: Enter the exact answer.

A: Let's find.

Q: Q4) Find the area of the region bounded by the lines (y=x) & (V=2-x) for xsO.

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Q: d the area (sq. units) covered by the line 2y = x + 6 from x1 = -8 to x2 = 0.

A: Given query is to find the area bounded by the curve.

Q: I = √²+¹dx Divide the integral into 5 equal parts (n=5) and obtain the numerical integral with the…

A: Trapezoidal rule: ∫abydx=h2(y0+2(y1+y2+y3+...+yn-1)+yn)  to approximate the integral: ∫abydx. Here,…

Q: Which integral represents the length of the graph of y = (x2-2) over the interval (3, 4]. Select…

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Q: When P = 3 Q3 Shade the area of the region bounded by, x² + y? 7 Hence, find the area of the…

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Q: Question * Using integration by parts and taking a > 0, the integral S, x In(ax)dx is equal to:

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Q: VI+ 25z°dz Evaluate the integral: + C

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Q: find the area of the portion of the cylinder x²+z²=16 lying inside the cylinder x²+y²=16

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. t/7t² + 8 dt…

A: Topic= Integration

Q: 3. Using the Trapezoid and Simpson's rules, solve the integral below: = (x In xdx a. 0,8 b. I=…

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Q: Use the Table of Integrals to evaluate the integral. 6 1 dx X 4x 7 Select the correct answer. The…

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Q: Using the substitution = the integral reduces to -1) 1 2p- dz 1/3

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 9et + 8e-* dx…

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Q: Q6. Using Trapezoidal Rule, evaluate the integral ſ³(3x² + 2x + 5) dx. Use Ax = 0.25.

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Q: 4X Q3/ Find the area of the region in the first quadrant enclosed by y = y In(x-1) %3D 8' y=1.

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Q: Q/ Evaluate the integrals :- 1 + Z

A: This question is based on indefinite integral.

Q: Q3/ Find the area of the region in the first quadrant that is bounded above by y = with respect to…

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Q: •V3 Evaluate (V3 – x? – 2|x|) dx by interpreting the integral geometrically.

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 5et + 2e-2 dx…

A: Given: ∫5ex+2e-x5ex-2e-xdxsubstitute  u=5ex-2x-x     then dudx=5ex+2x-x…

Q: Find the indefinite integral. Hint: Let u = 2 - Vx. (Remember to use absolute values where…

A: The given integral is ∫2+x2-xdx. Let u=2-x. Evaluate dx as follows.  du=-12xdx2xdu=-dx2-xdu=dx…

Q: Evaluate the integral using only methods taught in class, and simplify your answer. Do not ski…

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Q: Find the area of the region enclosed between f(x) = 0.9x²+ 6, g(x) = x, a =-8, and r = 4 Area =

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Q: 3. Determine the area above f(x) = x² + 2x + 3 and below the line y = 11.

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Q: Evaluate the integral using appropriate substitution. an NOTE: Enter the exact answer. dx +C…

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Q: What is the area of the region in terms of x? OA. (x2 - 11) dx+ | (10x) dx - V11 I (2-11- 1Ox) dr

A: question on area finding using definite integral

Q: 1 -dx Use the technique of completing the square to evaluate the following integral: J x2 - 6.x

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Q: Solve for what is asked. 1. Find the area of the region bounded by f(x) = x³, the x-axis, and the…

A: This question is based on application of Integration.

Q: Use substitution to find the indefinite integral. p(p +4)* dp P(p +4) dp=[

A: p+4=z is the substitution.