Area Find (i) the net area and (ii) the area of the following regions. Graph the function and indicate the region in question.
The region bounded by y = 6 cos 𝓍 and the 𝓍-axis between 𝓍 = ―π/2 and 𝓍 = π
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Area Find (i) the net area and (ii) the area of the following regions. Graph the function and indicate the region in question.
The region bounded by y = 6 cos 𝓍 and the 𝓍-axis between 𝓍 = ―π/2 and 𝓍 = π
Average distance on a parabola What is the average distance between the parabola y = 30𝓍 (20 ― 𝓍 ) and the 𝓍-axis on the interval [0, 20] ?
Evaluating integrals Evaluate the following integrals.
∫₁⁴ ((√v + v) / v ) dv
Consider the function
ƒ(t) = { t if ―2 ≤ t < 0
t²/2 if 0 ≤ t ≤ 2
and its graph shown below. Let F(𝓍) = ∫₋₁ˣ ƒ(t) dt and G(𝓍) = ∫₋₂ˣ ƒ(t) dt.
(f) Find a constant C such that F(𝓍) = G(𝓍) + C .
Evaluating integrals Evaluate the following integrals.
∫₀⁵ |2𝓍―8|d𝓍
Variations on the substitution method Evaluate the following integrals.
∫ (eˣ ― e⁻ˣ)/ (eˣ + e⁻ˣ) d𝓍