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MATH 101 HOMEWORK 4 Due on Wednesday Oct. 13. For full credit, show all work. Calculators are not allowed. 1. (4 marks) Find the area of the finite planar region bounded from above by the graph y = 3x − x2 and from below by y = |2x| − 6. 2. (8 marks) Evaluate the integrals: Z 8 3 (a) x2 · 4−x dx, 1 Z (b) x(tan−1 x)2 dx. 3. (8 marks) Evaluate the integrals (first make a substitution and then use integration by parts): Z 4 √ (a) e x dx, 1 Z (b) x5 cos(x3 ) dx. This homework covers Sections 5.6–6.1 of the textbook. Additional recommended exercises: Section 5.6, 5.7, as indicated earlier; Section 6.1, 1–30. 1