Question
The value of $\int x \cdot e^x d x$ will be
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Answer
self
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If direction ratios of a line are $1,1,-1$ then its direction cosines will be………
→Dfferentiation of $\cos (\sqrt{x})$ w.r.t. $x$ is ________ .
→If a line makes equal angles with the coordinate axes, then its direction cosines will be ___________ .
If $y=x+e^x$ then $\frac{d^2 y}{d x^2}=$ _________ .
→In a classroom, teacher explains the properties of a particular curve by saying that this particular curve has beautiful up and downs. It starts at 1 and heads down until $\pi$ radian, and then heads up again and closely related to sine function and both follow each other, exactly $\frac{\pi}{2}$ radians apart as shown in figure.
Based on the above information, answer the following questions.
→Based on the above information, answer the following questions.
- Name the curve, about which teacher explained in the classroom.
- Cosine
- Sine
- Tangent
- Cotangent
- Area of curve explained in the passage from 0 to $\frac{\pi}{2}$ is.
- $\frac{1}{3}\text{ sq.unit}$
- $\frac{1}{2}\text{ sq.unit}$
- ${1}\text{ sq.unit}$
- ${2}\text{ sq.units}$
- Area of curve discussed in classroom from $\frac{\pi}{2}$ to $\frac{3\pi}{2}$ is.
- -2 sq. units
- 2 sq. units
- 3 sq. units
- -3 sq. units
- Area of curve discussed in classroom from $\frac{3\pi}{2}$ to $2\pi$ is.
- 1 sq. unit
- 2 sq. units
- 3 sq. units
- 4 sq. units
- Area of explained curve from 0 to $2\pi$ is.
- 1 sq. unit
- 2 sq. units
- 3 sq. units
- 4 sq. units
Fill in the blanks:
The value of $\int\limits^\pi_{-\pi}\sin^3\text{x}\cos^2\text{x dx}$ is _______.
→The value of $\int\limits^\pi_{-\pi}\sin^3\text{x}\cos^2\text{x dx}$ is _______.
If A has a symmetric matrix then $B ^{ T } AB$ has ________ matrix.
→Fill in the blank.
The value of $\cos(\sin^{-1}\text{x}+\cos^{-1}\text{x}),$ where $|\text{x}|\leq1,$ is ______.
→The value of $\cos(\sin^{-1}\text{x}+\cos^{-1}\text{x}),$ where $|\text{x}|\leq1,$ is ______.
Fill in the blank.
The product of any matrix by the scalar _________ is the null matrix.
The product of any matrix by the scalar _________ is the null matrix.
If $A =\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right]$ and $\left| A ^3\right|=125$, then $\alpha=$ __________ .
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