(Step-by-Step) If f ∈ R and |f(x)| ≤ M for all x € [a, b], show that | ∫_a^bf(x)dx |≤
Question: If f \(\in \mathbb{R}\) and |f(x)| \(\le \) M for all x € [a, b], show that \[\left| \int_{a}^{b}{f(x)dx} \right|\le M(b-a)\]
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![[Steps Shown] Let g(x) = 0 if](/images/solutions/MC-solution-library-31051.jpg "[Steps Shown] Let g(x) = 0 if x ∈ [0, 1] is rational and")
[Steps Shown] Let g(x) = 0 if x ∈ [0, 1] is rational and
![[See Steps] Use the definition of derivative](/images/solutions/MC-solution-library-31052.jpg "[See Steps] Use the definition of derivative for: h(x)=√x, x>0")
[See Steps] Use the definition of derivative for: h(x)=√x, x>0
![[See Steps] Show that if a >](/images/solutions/MC-solution-library-31053.jpg "[See Steps] Show that if a > 0, then the convergence of the sequence")
[See Steps] Show that if a > 0, then the convergence of the sequence
(Solved) Suppose that f:R→ R is differentiable at c and that
![[Step-by-Step] If f:R→ R is differentiable at](/images/solutions/MC-solution-library-31055.jpg "[Step-by-Step] If f:R→ R is differentiable at c , prove that")
[Step-by-Step] If f:R→ R is differentiable at c , prove that
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