AP EAMCET · Maths · Area Under Curves
The area of the region under the curve \(y=|\sin x-\cos x|\), \(0 \leq x \leq \frac{\pi}{2}\) and above \(x\)-axis, is (in square units)
- A \(2 \sqrt{2}\)
- B \(2 \sqrt{2}-1\)
- C \(2(\sqrt{2}-1)\)
- D \(2(\sqrt{+1})\)
Answer & Solution
Correct Answer
(C) \(2(\sqrt{2}-1)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } y=|\sin x-\cos x|, 0 \leq x \leq \frac{\pi}{2} \\ & \text { Now, Area }=\int_0^{\frac{\pi}{2}}|\sin x-\cos x| d x \\ & =\int_0^{\frac{\pi}{4}}(\cos x-\sin x) d x+\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}(\sin x-\cos x) d x \\ & =[\sin x+\cos…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The equation of the curve passing through \(\left(\frac{\pi}{6}, 0\right)\) and satisfying the differential equation \(\left(e^y+1\right) \cos x d x+e^y \sin x d y=0\), isAP EAMCET 2017 Medium
- The direction cosines of the normal drawn to the plane passing through the points \((2,-1,5),(1,-3,4),(5,2,1)\) areAP EAMCET 2019 Easy
- If two sections of strengths 30 and 45 are formed from 75 students who are admitted in a school, then the probability that two particular students are always together in the same section isAP EAMCET 2019 Medium
- The number of ways that 8 beads of different colours be strung as a necklace isAP EAMCET 2002 Easy
- A random variable \(X\) has the following distribution
\begin{array}{lllllllll}
\hline \begin{array}{l}
Values of \\
X(x)
\end{array} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hlineP(X=x) \quad 0 & k & 2 k & 2 k & 3 k & k^2 & 2 k^2 & 7 k^2+k \\
\hline
\end{array}AP EAMCET 2018 Medium - 6 coins are tossed 320 times. The probability of getting 5 heads 2 times isAP EAMCET 2017 Easy
More PYQs from AP EAMCET
- If \(e_1\) and \(e_2\) are respectively the eccentricities of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and its conjugate hyperbola, then the line \(\frac{x}{2 e_1}+\frac{y}{2 e_2}=1\) touches the circle having centre at the origin, then its radius isAP EAMCET 2024 Medium
- An electronic assembly consists of two subsystems \(A\) and \(B\). Past testing procedures data show that probabilities of failure are \(P(A\) fails \()=0.2, P(B\) fails alone \()=0.15\), \(P(A \& B\) fail \()=0.15\). Then the probability that \(A\) fails alone is equal toAP EAMCET 2020 Easy
- If force \(=\frac{\alpha}{\text { density }+\beta^3}\), then the dimensional formulae of \(\alpha\) and \(\beta\) are respectivelyAP EAMCET 2025 Medium
- A circle passes through the centre of another circle \(x^2+y^2-3 x-4 y-1=0\) and whose centre is \((5,2)\). Then the equation of this circle is.........AP EAMCET 2020 Medium
- Two identical thin bar magnets, each of length \(l\) and pole strength \(m\), are placed at right angle to each other with north pole of one touching south pole of the other. The magnetic moment of the system isAP EAMCET 2020 Medium
- The solution of \(\left(1+y^2\right) d x-x y d y=0, y(1)=0\) represents a conic. Its eccentricity isAP EAMCET 2022 Medium