Mathematics

# Find the area of one of the curvilinear triangles formed by $y=\sin{x},y=\cos{x}$ and $x$ axis

##### SOLUTION
The point of intersection of  two curves $y=\sin{x}$ and $y=\cos{x}$ is at $\left(\dfrac{\pi}{4},\dfrac{1}{\sqrt{2}}\right)$

Required Area$=\displaystyle\int_{0}^{\tfrac{\pi}{4}}{\sin{x}dx}+\int_{\tfrac{\pi}{4}}^{\tfrac{\pi}{2}}{\cos{x}dx}$

$=\displaystyle\left[-\cos{x}\right]_{0}^{\frac{\pi}{4}}+\left[\sin{x}\right]_{\frac{\pi}{4}}^{\frac{\pi}{2}}$

$=-\left[1-\dfrac{1}{\sqrt{2}}\right]+\left[\dfrac{1}{\sqrt{2}}-1\right]$

$=2\left[\dfrac{1}{\sqrt{2}}-1\right]$

$=\dfrac{2}{\sqrt{2}}-2$

$=\dfrac{2}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}-2$

$=\sqrt{2}-2$sq.unit

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Subjective Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Subjective Medium
Integrate $\displaystyle \int \dfrac{x^{2}}{x^{3}+1}\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\underset{n\rightarrow\infty}\lim \displaystyle \sum_{r=1}^{n}\dfrac{1}{\sqrt{4n^{2}-r^{2}}} =$
• A. $\dfrac\pi2$
• B. $\dfrac\pi3$
• C. $\dfrac\pi5$
• D. $\dfrac\pi6$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Calculate:
$\int (x^{3/2} - x^{1/2} + 5x) dx$.
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• B. $\dfrac{2x^{5/2}}{5}-\dfrac{x^{3/2}}{4}+\dfrac{5}{2}x^2+c$
• C. $\dfrac{x^{5/2}}{5}-\dfrac{2x^{3/2}}{3}+\dfrac{5}{2}x^2+c$
• D. $\dfrac{2x^{5/2}}{5}-\dfrac{2x^{3/2}}{3}+\dfrac{5}{2}x^2+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve:

$\displaystyle\int_{0}^{\pi/2} \sin x \cos x\ dx$

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