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
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
