2022 Chp 6B Applications of Integration BMQ Solutions (RVHS)

H2 Mathematics (9758) JC1 River Valley High School Mathematics Department, 2022 Ch 6B Applications of Integration (Solutions to Tutorial and Assignment) 1 Solutions to Tutorial 6B: Applications of Integration Basic Mastery Questions 1. Evaluate exactly the following integrals by using the given substitutions (and use a GC to check your answers): (a) 2 3 2 2 1 d1 xx x  , using u = 1 x (b) 1 40 2 d 1 x x x, using  1 2tan x  Solution:

H2 Mathematics (9758) JC1 River Valley High School Mathematics Department, 2022 Ch 6B Applications of Integration (Solutions to Tutorial and Assignment) 2 2. Evaluate exactly the following integrals using integration by parts substitutions (and use a GC to check your answers): (a) 2 3 0 e dxx x    (b)   e 2 1 ln dx x Solution for 2(a): Solution for 2(b):

H2 Mathematics (9758) JC1 River Valley High School Mathematics Department, 2022 Ch 6B Applications of Integration (Solutions to Tutorial and Assignment) 3 3. (a) Evaluate π π sin dx x . (b) Find the area of the region bounded by the curvexy sin , the x-axis and the lines 0x and πx . (c) Find the area of the region bounded by the curvexy sin , the x-axis and the lines πx and 0x . Compare with the answer in (b). (d) Deduce the area bounded by the curvexy sin , the x-axis and the lines πx and πx . Compare with the answer in (a). Solution: 4. Find the volume generated by revolving the region in the first quadrant, bounded by the curve y = x2 + 1, the y-axis and the line y = 5, about (i) the x-axis, (ii) the y-axis through 4 right angles. Solution: