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Test 1 Review (Calc II)Questions and and answers (1)
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Test 1 Review (Calc II)Questions and and answers (1)
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Test 1 Review (Calc II)∫√u -✅✅-(2/3)u^3/2
Derivative of 2/x - ✅✅--2/x²
Derivative of sec²(x) - ✅✅-tan(x)
Derivative of arctan(x) - ✅✅-1/1+x²
antiderivative of 1/1+x² - ✅✅-tan⁻¹(x)
antiderivative of tan(x) - ✅✅-ln(|sec(x)|)
✅✅-(1/b-a) ∫f(x)dx
average value of a function on an interval [a,b] -
What rule does "Integration by Parts" correspond to? - ✅✅-Product Rule
Integration by parts basic formula - ✅✅-∫udv = uv-∫vdu
Integration by parts steps? - ✅✅-1. Choose a function for u
2. The remainder of the integrand is dv
3. Differentiate u to get du
4. Integrate (anti-differentiate) dv to get v
5. Substitute into formula
6. Anti-differentiate
7. Repeat if needed
✅✅-(1/3)e^3x
Anti-derivative of e^3x -
Derivative of e^3x - ✅✅-3e^3x
✅✅
dv = cos(4x)
v=? - -(1/4)sin(4x)
Anti-derivative of (3/4)sin(4x)? -✅✅--(3/16)cos(4x)
Integration by parts w/definite integrals formula - ✅✅-
Derivative of ln(6x+1) - ✅✅-6/6x+1
Reason substitution wouldn't work - ✅✅-u and du wouldnt cancel part of the
equation
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