MTH405_Wk_10_Tutorial

# MTH405_Wk_10_Tutorial - MTH405 Wk 10 Tutorial 1 Integrate...

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Unformatted text preview: MTH405 Wk 10 Tutorial 1. Integrate the following. ˆ ˆ 2 a.) x dx ˆ c.) ˆ ˆ 1 dx x2 x dx f.) 2. 4 cos xdx ˆ  x + x2 dx g.) i.) xdx ˆ ˆ ˆ √ d.) −1 e.) x3 dx b.)  3x6 − 2x2 + 7x + 1 dx h.) t2 − 2t4 dt t4 Solve the following initial value problems (IVP). dy dx dy (b) dx dy (c) dx dy (d) dx (a) (e) dy dx Remark. = cos x, y(0) = 1.  = sin t + 1, y π3 = 12 . √ = 3 x, y(1) = 2 = x+1 √ x , y(1) = 0 = sec2 t − sin t, y π 4  = 1. Given an IVP, the procedure is the following: dy = g(x) dx dy = g(x)dx ˆ ˆ dy = g(x)dx y = G(x) + c then use the initial value condition to nd the value of c. 1 3. Evaluate the following integrals using the indicated u-substitutions. ˆ 2x(x2 + 1)23 dx; u = x2 + 1 a.) ˆ cos3 x sin xdx; b.) u = cos x ˆ √ 1 √ sin xdx; x ˆ 3xdx d.) √ ; 2+5 4x ˆ e.) sec2 (4x + 1)dx; ˆ p f.) y 1 + 2y 2 dy; c.) 4. u= √ x u = 4x2 + 5 u = 4x + 1 u = 1 + 2y 2 Evaluate the following integrals by using the method of Integration by Parts. ˆ ˆ −2x a.) xe dx ˆ c.) ˆ x sin 3xdx x2 cos 2xdx d.) ˆ e.) xe3x dx b.) ˆ √ x ln xdx f.) ex sin xdx h.)e3x cos 2xdx x ln xdx ˆ g.) 2 ...
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• Spring '16
• Alveen Chand
• dx

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