MAT 210 Lecture Notes - Lecture 28: Mrs. Ples

1. In each case write down the most general anti?derivative associated with the given function. (a) f(x)=x^2 - 3cos(2x)+1 x Element R, (b) g(x)=(13x - 1)^7+ root x-1 x less than or equal to 1, (c) h(x) = (x + 1)sin(x^2+2x) ? 1/x^2. X not equal to 0.2. Calculate the area of the finite region bounded by tile parabolas given by y = (x + 1)(x - 1), and y = -(1 + 4x + x^2) 3. For what value of k is the area under the graph of y = 3x^2 + 4kx between x = 0 and x = 1, equal to 3? 4. Evaluate (a) Integrate limit between 0 to 1 x(x^3+2x +1)dx, (b) Integrate limit between 0 to Pi x + cos(x) sin^2(x) dx.

puut pait (a) using left endpoints (c) Repeat part (a) using midpoints. (d) From your sketches in parts (a)-(c), which appears to be best estimate? C 5. Use [Area = nim Rn = nimo[f(x1)0x + f(x2)0x + for the area under the graph offas a limit. Do not evaluate the limit. f(x)- 3. + f(xn)예 to find an expression 2X , 1 x 6, Express the limit linn2%-Δxias a definite integral on [0,11. 1+xi (7) *Use [1,f(x)dx=limo Σ.1 f(xi)aZG Δ.b -a , xt = a + i Δχ| to evaluate the integral : 0 8. Evaluate the integral 3(1 + v9 - x2)dx by interpreting it in terms of areas. ㈠9. Iff,f(x)dx=37 and fog(x)dx= 16, findf(2f(x)+3g(x))dx. 10. Use Part I of the Fundamental Theorem of Calculus to find the derivative of (a) h(x)=「Int dt and (b) y = tan θ d8.

a2bdb10147299d#10016 https://www MATH1160 JMinear Aug18 Sat Homework: Practice HW9 Score: 0 of 1 pt 2 of 10 (6 comp 4.3.9 Find the area between the curve and the x-axis over the indicated interval y 100-x I-10, 10] The area under the curve is (Simplify your answer) Enter your answer in the answer box and then click Check Answer Clear Al All parts showing

MATH1160 JMinear Aug18 Sat Homework: Practice HW9 Score: 0 of 1 pt 4.3.13 3 o Find the area between the curve and the x-axis over the indicated interval. y [1.6] The area under the curve is (Type an exact answer.) Enter your answer in the answer box and then click Check Answer

MATH1160 JMinear Aug18 Sat Homework: Practice HW9 Score: 0 of 1 pt 4.4.3 Find the area under the graph of f over the interval !-23) 2xX 1 The area is (Simplify your answer) Enter your answer in the answer box and then click Check Answe All parts showing

MATH1160 JMinear Aug18 Sat Homework: Practice HW9 Score: 0 of 1 pt Bus Econ 4.3.63 8 of 10 (6 com A company estimates that its sales will grow continuously at a rate given by the function S'()-17e where S'() is the rate at which sales are increasing, in dollars per day, on day t a) Find the accumulated sales for the first 8 days. b) Find the sales from the 2nd day through the 5th day. (This is the integral from 1 to 5.) a) The accumulated sales for the first 8 days isS Round to the nearest cent as needed.) Enter your answer in the answer box and then click Check Answer Cleat All