7. Express the limits lim sin(x: Aras a definite integral on the interval [0.2) and then...
Express the limit as a definite integral on the given interval. lim η Σ X; -ΔΧ, +7 [1, 9] (x)2 + = 1 dx 1
Express the limit as a definite integral on the given interval. lim n00 1 = 1 X; In(1 + x2) Ax, [2, 4] SI dx
1. Express the following limits as a definite integral: (a) lim 19–1 xịIn(1 + xi;?))Ax (2,6] (b) lim E?a. Co Ax [TT, 21) n00 m Li=1 Xi in COSXį n00
Express the Arc Length of the given curve on the specified interval as a definite integral. Don't evaluate, just set it up. y=ez) on (0.2]
A. Express the limit as a definite integral on the given interval. B. Use the form of the definition of the integral to evaluate the integral. n Š lim n-> Xi Ax, [1, 3] (xi +13 * 2 i=1 3 6 (2x - x2) dx
Question 4 4.1 Express the limit as a definite integral on the given integral: 1-x} Ax , [2,6] lim Σ=1 a. (2 Marks) n->00 4+x} lim (?-1 - Ax ,[1,3] (xi) - 4 b. (2 Marks) n->00 4.2 Evaluate the following expressions. Show your calculations. $=1(2p – p2) b. En-o sin a. (2 Marks) пп (2 Marks) 2 C. 2m +2 53 Lm=1 3 (2 Marks) [Sub Total 10 Marks]
8. Write down a definite integral (but do not evaluate) that produces the following limit of sums using the definition of definite integral: b) lim 61 k-l 8. Write down a definite integral (but do not evaluate) that produces the following limit of sums using the definition of definite integral: b) lim 61 k-l
Express the following limit as a definite integral. n 1 lim P10 k=1 -Axk where P is a partition of [3,5] 5 The definite integral is si dx. 3
ππ Express the limit lim 2 (2csco) 4Xx as a definite integral where P is a partition of 63 (D (Type exact answers, using π as needed.) ππ Express the limit lim 2 (2csco) 4Xx as a definite integral where P is a partition of 63 (D (Type exact answers, using π as needed.)
os. Define R as the region bounded by the graph of y2x-x' and by the axis over the interval [0.21 Find the volume of the solid of revolution formed by revolving Ruround the y-axis. Hint: Use Shell Method. 16 pts) 6. Find the average value, so of the function /(x) = cos x over the interval (0, 2) and find e such that f(e) equals the average value of the function over [0, 2x) 15 pts] 7. Express the limits...