CALC 2 EXAM STUDY GUIDE ANSWERED -2

CALC 2 EXAM STUDY GUIDE ANSWERED #2
∫Udv = - correct answer uv - ∫vdu

Sin²θ + cos²θ = - correct answer 1

1 + tan²θ = - correct answer sec²θ

1 + cot²θ = - correct answer csc²θ

Sin(2θ) = - correct answer 2sinθcosθ

Cos(2θ) = - correct answer 2cos²θ - 1 or cos²θ - sin²θ

Cos(2θ) = - correct answer 1 - 2sin²θ

∫tanxdx = - correct answer ln|secx| + c

∫cotxdx = - correct answer ln|sinx| + c

∫secxdx = - correct answer ln|secx + tanx| + c

∫cscxdx = - correct answer ln|cscx - cotx| + c

∫sin²xdx = - correct answer ½x - ¼sin(2x) + c

∫cos²xdx = - correct answer ½x + ¼sin(2x) + c

∫1/(x² + a²)dx = - correct answer (1/a)tan⁻¹(x/a) + c

√(a² - x²) = - correct answer x = asinθ

√(x² + a²) = - correct answer x = atanθ

√(x² - a²) = - correct answer x = asecθ

Trapezoidal rule: from a to b ∫f(x)dx ≈ - correct answer ½δx[f(x₀) + f(xⁿ) + 2∑f(0<x<n)]
Where δx = (b-a)/n and xⁿ = a + nδx

∫f(x) from -∞ to ∞ = - correct answer ∫f(x) from ⁻∞ to a + ∫f(x) from a to ∞

∫f(x) from a to ∞ = - correct answer lim t->∞ of ∫f(x)dx from a to t

From 1 to ∞, ∫1/xⁿdx (n>1)(convergent or divergent) - correct answer convergent

From 1 to ∞, ∫1/x²dx (convergent or divergent) - correct answer convergent