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Evaluate sinº z (cos a) ºdt. Select one: a sinc COS I +6 b. None of these O c.sec + cos2 +C O d. csc + cos X +
1. cos 4 x-sinº x = cos 2x 6 6 2. sin x + COS x = 1-3sin ?x cos” x 3. cos 2x = 1-tanx 1+tanx 4. 2sinx cosx = cos(x-y) – cos (x+y)
11. Verify the identity cosx csc? x = csc? x – sinº x– 2. 12. Verify the identity (cos (x + y)][cos (x - y)] = cosx – sin? y.
Calculate the definite integrals below. + arctan) (u) . ܫܐ). (o) V1 + cos 4.cda -
4. (10 points) Find the general indefinite integral. (a) [1+ya+z dir T (b) sinº(@)cos(0) do » sin®®) (Make the substitution u = sin(0))
integration by parts 8. Evaluate the following integrals S cos cos(*)sinº (x)dx b zsin (x)dx
Find in 4e2" sinº(42)|1
3. [6 marks] Solve the IVP: cos x + y sin x = sinº x, y(0) = 2.
9. Determine the area of the region bounded by the graph of f(x) = sinº(5x) cos(5x) and the x-axis between x = -0.2262 and x = 0.2953, giving your answer to 4 decimals. A) 0.0584 B) 0.0634 C) 0.0684 D) 0.0734 E) 0.0784
Evaluate (T/4 sinº (2x) cos (2x) dx. 17/12 Round your answer to 2 decimal places if necessary. For what value of kis the area under the graph of y = 3x2 + 4kx between x = 0 and x = 1, equal to 3? Round your answer to 2 decimal places if necessary. Evaluate 1 x (x + 2x + 1) dx. Jo Evaluate cos (T) da. Cvaluate 5 (23 + 4) dx.