The area (in sq. units) bounded between the curves y=e^xcos⁡x and y=e^xsin⁡x from x=(π)/4 to x=(π)/2 is

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MARKS Content Team · Accepted Answer

Correct answer: (B) (e^(π4))/(√2). As sin⁡x>cos⁡x, ∀x∈(π)/4,(π)/2 ⇒e^xsin⁡x>e^xcos⁡x Thus the required area is A=∫(π)/4(π)/2e^xsin⁡x-e^xcos⁡xdx =-∫(π)/4(π)/2e^xcos⁡x+-sin⁡xdx =-e^xcos⁡x(π)/4(π)/2 =− 0−e^(π 4) ⋅1/(√2) =(e^(π4))/(√2) As∫e^x f x +f^(′) x dx=e^x ⋅f x +C

The area (in sq. units) bounded between the curves $y = e^{x} \cos x$ and $y = e^{x} \sin x$ from $x = \frac{π}{4}$ to $x = \frac{π}{2}$ is

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More Area Under Curves Questions

The area (in sq. units) bounded between the curves y=excos⁡x and y=exsin⁡x from x=π4 to x=π2 is

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More Area Under Curves Questions

The area (in sq. units) bounded between the curves $y = e^{x} \cos x$ and $y = e^{x} \sin x$ from $x = \frac{π}{4}$ to $x = \frac{π}{2}$ is