Transcription of Integration Worksheet - Substitution Method Solutions
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Integration Worksheet - Substitution Method Solutions
Integration Worksheet - Substitution Method Solutions The following are Solutions to the Math 229 Integration Worksheet - Substitution Method . Here's the link to that Worksheet Z. 1. (5x + 4)5 dx (a) Let u = 5x + 4. 1. (b) Then du = 5 dx or du = dx. 5. (c) Now substitute Z Z. 5 1. (5x + 4) dx = u5 du 5. Z. 1 5. = u du 5. 1 6. = u +C. 30. 1. = (5x + 4)6 + C. 30. Z. 2. 3t2 (t3 + 4)5 dt (a) Let u = t3 + 4. (b) Then du = 3t2 dt (c) Now substitute Z Z. 2 3 5. 3t (t + 4) dt = (t3 + 4)5 3t2 dt Z. = u5 du 1 6. = u +C. 6. 1 3. = (t + 4)6 + C. 6.. Z. 3. 4x 5 dx 1. Integration Worksheet - Substitution Method Solutions (a) Let u = 4x 5. 1. (b) Then du = 4 dx or du = dx 4. (c) Now substitute . Z Z. 1. 4x 5 dx = u du 4. Z. 1 1/2. = u du 4. 1 3/2 2. = u +C. 4 3. 1. = (4x 5)3/2 + C. 6. Z. 4. t2 (t3 + 4) 1/2 dt (a) Let u = t3 + 4. 1. (b) Then du = 3t2 dt or du = t2 dt 3. (c) Now substitute Z Z. 1/2. 2 3.
Integration Worksheet - Substitution Method Solutions (a)Let u= 4x 5 (b)Then du= 4 dxor 1 4 du= dx (c)Now substitute Z p 4x 5 dx = Z u 1 4 du = Z 1 4 u1=2 du 1 4 u3=2 2 3 +C = 1
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