Let f : 0 , 2 → R be a function which is continuous on 0 , 2 and is differentiable on 0 , 2 f 0 = 1 . Let F x = ∫ 0 x 2 f t d t for x ∈ 0 , 2 . If F ' x = f ' x for all x ∈ 0 , 2 , then F 2 equals

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Let f : 0 , 2 &#8594; R be a function which is continuous on 0 , 2 and is differentiable on 0 , 2 f 0 = 1 . Let F x = &#8747; 0 x 2 f t d t for x &#8712; 0 , 2 . If F ' x = f ' x for all x &#8712; 0 , 2 , then F 2 equals

Quantrex Academy · Accepted Answer

Correct answer: B. e 4 - 1

F 0 = 0 F ' x = 2 x &#160; f x = f ' x f x = e x 2 + c f x = e x 2 &#160; &#160; &#8757; &#160; &#160; &#160; f 0 = 1 F x = &#8747; 0 x 2 e x &#160; d x &#160; F x = e x 2 - 1 &#160; &#160; &#8757; &#160; F 0 = 0 &#8658; &#160; F 2 = e 4 - 1

Let f : 0 , 2 → R be a function which is continuous on 0 , 2 and is differentiable on 0 , 2 f 0 = 1 . Let F x = ∫ 0 x 2 f t d t for x ∈ 0 , 2 . If F ' x = f ' x for all x ∈ 0 , 2 , then F 2 equals

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More from Differential Equations

Let f : 0 , 2 &#8594; R be a function which is continuous on 0 , 2 and is differentiable on 0 , 2 f 0 = 1 . Let F x = &#8747; 0 x 2 f t d t for x &#8712; 0 , 2 . If F ' x = f ' x for all x &#8712; 0 , 2 , then F 2 equals

Options

Correct answer

Step-by-step solution

More from Differential Equations

Let f : 0 , 2 → R be a function which is continuous on 0 , 2 and is differentiable on 0 , 2 f 0 = 1 . Let F x = ∫ 0 x 2 f t d t for x ∈ 0 , 2 . If F ' x = f ' x for all x ∈ 0 , 2 , then F 2 equals