Question

Calcule as integrais
a)∫₁⁴ (√x - 1 dx
√x)

b)∫₀² dx
√16-x²

c)∫ 3x+11 dx
x² -x -6

Answer 1

Boa tarde

a)

f(x) = (√x - 1)/√x

integral

F(x) = ∫ (√x - 1)/√x dx

F(x) = x - 2√x + C

F(4) = 4 - 2√4 = 4 - 4 = 0

F(1) = 1 - 2√1 = 1 - 2 = -1

I = F(4) - F(1) = 0 - (-1) = 1

b)

f(x) = 1/√(16- x^2)

F(x) = ∫ 1/√(16- x^2) dx

F(x) = arcsen(x/4) + C

F(2) = arcsen(2/4) = 0.52359

F(0) = arcsen(0) = 0

I = F(2) - F(0) = 0.52359

c)

F(x) = ∫ (3x + 11)/(x^2 - x - 6) dx

F(x) = 4ln(3 - x) - ln(x + 2) + C