Calc 2: Exam 1 Study Guide With 100% Correct Answers | Verified

Calc 2: Exam 1 Study Guide With 100%
Correct Answers | Verified
∫udv = CORRECT ANSWERS uv - ∫vdu

sin²θ + cos²θ = CORRECT ANSWERS 1

1 + tan²θ = CORRECT ANSWERS sec²θ

1 + cot²θ = CORRECT ANSWERS csc²θ

sin(2θ) = CORRECT ANSWERS 2sinθcosθ

cos(2θ) = CORRECT ANSWERS 2cos²θ - 1 or cos²θ - sin²θ

cos(2θ) = CORRECT ANSWERS 1 - 2sin²θ

∫tanxdx = CORRECT ANSWERS ln|secx| + C

∫cotxdx = CORRECT ANSWERS ln|sinx| + C

∫secxdx = CORRECT ANSWERS ln|secx + tanx| + C

∫cscxdx = CORRECT ANSWERS ln|cscx - cotx| + C

∫sin²xdx = CORRECT ANSWERS ½x - ¼sin(2x) + C

∫cos²xdx = CORRECT ANSWERS ½x + ¼sin(2x) + C

∫1/(x² + a²)dx = CORRECT ANSWERS (1/a)tan⁻¹(x/a) + C

√(a² - x²) = CORRECT ANSWERS x = asinθ

√(x² + a²) = CORRECT ANSWERS x = atanθ

√(x² - a²) = CORRECT ANSWERS x = asecθ

Trapezoidal rule: From a to b ∫f(x)dx ≈ CORRECT ANSWERS ½Δx[f(x₀) + f(xⁿ) +
2∑f(0<x<n)]
where Δx = (b-a)/n and xⁿ = a + nΔx

∫f(x) from -∞ to ∞ = CORRECT ANSWERS ∫f(x) from ⁻∞ to a + ∫f(x) from a to ∞

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