(b) Use integration to find the net area between f(x)=sin(x) and the x-axis, from x=0 to x= 5%. (c) Use integration to find the total area between f(x)=sin(x) and the x-axis, from x=0 to x = 5%.

Q: Evaluate the integral. (Use C for the constant of integration.) (x2.8 + x-1.2) dx

A: Power rule

Q: Find the area of the region that is enclosed between the curves a = y and x= y - 2 integrating with…

A:

Q: 38. Use numerical integration to estimate the value of dx. п

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 8 dx x + 8 +

A: We first rationalize the…

Q: Evaluate the integral. (Use C for the constant of integration.) x2 – 49 dx

A: Topic - indefinite Integration

Q: Evaluate the integral. (Use C for the constant of integration.) 10e-0.7x dx

A:

Q: Question Using integration by parts, the integral f(9x 3)e*dx is equal to:

A: Given: ∫(9x-3)e3xdx Integration by parts: ∫uv dx=u∫v dx-∫dudx∫v dxdx Where, v and u functions of x

Q: Evaluate the integral by u-substitution. (Use C for the constant of integration.) sin7(x)…

A:

Q: 2. When applying the formula for integration by parts, how do you choose the u and dv? How can you…

A: Choose u for logarithmic, inverse, algebraic, trigonometric and exponential function and the others…

Q: Evaluate the integral. (Use C for the constant of integration.) (8x3 − 6x2 + 8x +

A:

Q: Use the basic integration rules to find or evaluate the integral. (Use C for the constant of…

A:

Q: For evaluating the integral x tan-lr dx, we apply integration by parts technique with the…

A:

Q: Use the basic integration rules to find or evaluate the integral. (Use C for the constant of…

A: Solving the problem my method of integration.

Q: Find the integral xn ln x dx; n ≠ −1, n real. (Use C for the constant of integration.)

A: we have to use integration by parts ∫uvd=u∫vd-∫du∫vdd  and ∫xndx=xn+1n+1+c where c is the…

Q: Use integration by parts to find the integral. (Use C for the constant of integration.)

A: Consider the provided integral,

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) a + bx5 dx V 6ax + bx6

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (x6 − 6x2)4(x5 − 2x) dx

A: From the given problem:   I=∫x6− 6x24x5 − 2x dx...(1)   First simplifying:…

Q: valuate the indefinite integral. (Use C for the constant of integration.) 6 - x2 dx

A: We need to substitute for this integration

Q: Evaluate the integral. (Use C for the constant of integration.) csc*x cotºx dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 19xe2x/(1 + 2x)2 dx

A: To evaluate ∫19xe2x1+2x2dx

Q: Evaluate the indefinite integrals using Substitution. (use C for the constant of integration.) a) x…

A: To evaluate:a) ∫1x+9dxb) ∫12-4x+5dx

Q: 12. Use integration to determine the average value of y = a² sin(b²x) between x = %3D 0 and x = b² *…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (tan²(x) tan^(x) dx

A: Given       I=∫7tan2x++tan4xdx      = 7∫tan2x1+tan2xdx      = 7∫tan2x.sec2x dx∵sec2x-tan2x=1

Q: Evaluate the integral. (Use C for the constant of integration.) 75 – 10x – x² dx

A:

Q: Using integration by parts, the integral Vx In x dx equals:

A: Given ∫1ex lnx dx To evaluate integral using by parts rule

Q: 12. Use integration to determine the average value of y = a² sin(b²x) between x = 0 and x = b2

A: Let's find.

Q: In the diagram below, the region between the graphs of y=2 sin¬x and y=rx, in the first quadrant, is…

A: Finding the area of the shaded region

Q: Find the integral. (Use C for the constant of integration.) (x6 + 5-×) dx

A: In this question, we need to find the integral of given function.

Q: (x2 + 7)(x1/2 − 7) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.)   (x2 + 4x) cos(x) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) ln(√x) dx

A: I = ∫ln(x)dxUsing,     ln ab=b ln aI  = ∫ln(x)12dxI =12∫ln(x) dx

Q: Evaluate the integral. (Use C for the constant of integration.) X + 14 dx + 2x + 5

A: Topic - integration

Q: Evaluate the integral. (Use C for the constant of integration.) 21 dx 3x + xVx + x/x

A: Explained below

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) a + bx5 dx 6ax + bx6

A: Given the following integral:

Q: Evaluate the integral. (Use C for the constant of integration.) e2x dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x2 + 16x + 1 (x2 + 1)2…

A: We have to find integral.

Q: Find the indefinite integral. (Use C for the constant of integration.) x* + x – 25 dx x2 + 5 1 3 -…

A:

Q: Use integration by parts to find the integral. (Use C for the constant of integration.)

A: Given:

Q: Evaluate the integral. (Use C for the constant of integration.) x2 - 64 dx

A: The given integral is ∫x2-64x3dx. Let us assume u=x2-64 and v'=1x3. Differentiate u with respect to…

Q: Calculate the integral. (Use C for the constant of integration.)   dx x   4x4 − 1

A:

Q: Use trigonometric substitution to find or evaluate the integral. (Use C for the constant of…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 16 tan (x) sec (x) dx C must be in…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 10 dx 5x + x/x

A:

Q: Use Romberg integration to approximate √² 2x² + x − 1 dx. Compute the Romberg table until Rij-…

A: The Final diagonal element is always consider the best estimate of the integral  I=∫abf(x)…

Q: Use integration by parts to derive a reduction formula for x"e- dx. Jse the result from part 1 to…

A:

Q: Evaluate the integral. (Use C for the constant of integration.)   (x2.8 + x−1.3) dx

A:

Q: Using integration by parts, the integral f In(16x*) dx is equal to:

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 25x-5 dx

A:

Q: The value of 'h' for evaluating the integral 8. Si f(x) dx using the numerical integration…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x^2/(49 − x^2)^1/2 dx

A: I =  ∫x249-x2 dx   I = ? Formulas: 1. ∫dxa2 - x2 = sin-1xa + c 2. ∫a2 - x2 dx = xa2 - x22 +…