1) 2) Evaluate the integrals of the functions graphed by using the formulas for areas of...
Given the function graphed below, evaluate the definite integrals. 4 3 2 1 -1 1 2 3 4 5 -] - 6 -3 7 f(x)dx = Preview 5 sm)dor = Preview
EXAMPLE 4 Evaluate the following integrals by interpreting each in terms of areas. (a) y=V25-2 lov ✓ 25 - 2 dx or 10 + y = 25 (x - 3) dx SOLUTION (a) Since Rx) = V25 - x2 > 0, we can interpret this integral the area under the curve y = 25 - X2 from 0 to But we get x2 + y2 = 25, which shows that the graph of ris a quarter-circle with radius in the...
Given the function graphed below, evaluate the definite integrals. 4 3 2 1 2 3 4 5 6 7 8 -2 -3 -4 Preview [ f(z)dx = [ f(a)dx = Preview
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...
Q3 1. For the following, in (a) sketch the graphs of the functions and in (a) and (b) find the areas as indicated (a) the area bounded by y = f(x) = x2 - 4x + 5 and y = g(2) = 2x - 3. (b) the area of the region that is common to r= 3 cos(0) and r = sin(). See sketch below. 2. Consider the region bounded by y? = 4, y = 2 and r =...
Piecewise Functions Graph: f(x) = x +5 if x 21 if x< 1 Calculate: 11) f(1) = 12) f(-3) = 13) f(2)= Functions: 1) Find g(2)= 1963 2) Find x-intercepts 3) Find y intercept 4) Find Domain of g 5) Find Range of g 6) For what value of x is g(x) = 0? 7) For what value of x is g(x) = 2? 8) Interval where g is decreasing - 9) Relative Maximum Point
3. Using the graph off compute the definite integrals (use known geometric formulas). 2 4 (n) (2) de (w) | sle)dr = S $12)de - [ Педаг . (e) 4. Using the graph of g compute the definite integrals. area 3 arca-6 6 7 5 area (b) (a) [*ola) dr = 9(x) dx = (c) (a)dx (d) (Circle one) ne) . 9(1) dr = positive / negative / zero 2
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
Using trigonometric identities and substitution, evaluate the following integrals: 1. S sin5 x dx 2. Shamrzdx 3. S V4 – 9x2dx 4. Sýsin? x dx 5. S 1 dx x2 +81
2. Evaluate the following integrals. (a) [5 marks] | el cos 4xdx -1 x (b) [5 marks] / cosdx -x³+3x²-x- dr. 1dx (c) [10 marks] (п -3)(12+2) 4 (d) [5 marks]/ dx V4-5x-2x2 dx cosh x-sinh x (e) [5 marks]] (Give the final answer in terms of e.)