Use the graph of y=f(x) to calculate the integrals below. 30 3 (a) [f(x)dx= ] SAL
Use geometry to evaluate the following definite integrals, where
the graph of f is given in the figure.
LLLLL y=f(x) 1 1 2 3 4 5 6 7 8 x | f(x)dx
Consider the graph of the functi y = f(x) 14 6 Evaluate the following integrals by interpreting them in terms of areas: [* f(e)dx = 4 a» [° s(m) do = 6 <-> ["s(e) dx = 8 (0 [° f(x) dx = 12 = 12
8. Given the graph of the function f, use area to compute f(x) dx. y y= f() 3 2 1 2 -1 4 ce
Given the graph of f(t), below, compute the indicated definite integrals. (4,2) 3 4 5 6 (a) ["f(x) dx (b) ſs(e) de (e) $* $(x) dx (a) [5(e) de
4. Given the integrals, [° 8(x) dx =-7, 5*8(x)dx = 6 and 5*g(x) dx = 10, use the properties of integrals to determine the value of the integrals below. a) [°(f(x)+g(x)\dx b) ſ 8(x)dx (4 pts cach) c) $39(x)dx a [ f(x)dx
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)...
w )) 4. (a) (+3) Use the graph to estimate li f()dx – 53 g(x)dx. (b) (+3) Using the graph order the following from least to greatest; g(0), and (3) Lean () dx, S(-2), 8(O)
3) Suppose F(x) is an antiderivative of f(x). Use the graph of the functionf(x) below to answer the following: flx) a) Approximate f'(6), and explain/show how you arrived at your answer 6 4 3 2 b) Explain/show why F'(6) 2 1 2 3 4 5 6 7 c) Approximate o f(x)dx, and explain/show how you arrived at your answer. d) Explain/show why f'(x)dx-3.
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
Evaluate the integrals.
Íx” dx = ſx=3 dx = (x-3) secx tan x dx = j(x?- Var)dx=