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Please check my answers
a) I know that e^x^3 > 0 and for all x ∈ [-1, 1], so we have ∫[-1 to 1] e^x^3 dx > 0. But how would you explain in words?
b) For all x ∈ [0, 1] , 0 ≤ x^2 ≤ x , so e^0 ≤ e^x^2 ≤ e^x
Therefore
∫[0 to 1] e^0 dx ≤ ∫[0 to 1] e^x^2 dx ≤ ∫[0 to 1] e^x dx
where do i go from here?
thanks.
Please check my answers
a) I know that e^x^3 > 0 and for all x ∈ [-1, 1], so we have ∫[-1 to 1] e^x^3 dx > 0. But how would you explain in words?
b) For all x ∈ [0, 1] , 0 ≤ x^2 ≤ x , so e^0 ≤ e^x^2 ≤ e^x
Therefore
∫[0 to 1] e^0 dx ≤ ∫[0 to 1] e^x^2 dx ≤ ∫[0 to 1] e^x dx
where do i go from here?
thanks.