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Evaluate $I=\int\limits_0^{\infty} e^{-2t} + (\dfrac {\sin ht \sin t}t dt$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Find the area using double integration where the region of integration is bounded by the curves $qxy = 4$ and $2x + y = 2.$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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The area bounded by $|y| = \sqrt x$ and $\sqrt x = |y| + 2$ is equal to A. $\dfrac {22}3$ B. $\dfrac {20}3$ C. $\dfrac {16}3$ D. $\dfrac {14}3$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Evaluate $\int\limits_{0}^{\infty} \frac{cos6t - cos4t}{t} dt$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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$\dfrac {dy}{dx}+x\sin zy =x^3\cos^2y$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Evaluate $\int\limits\int\limits x^2 \space dxdy$ where A is the region in the first quadrant bounded by the hyperbola $xy=16$ and the line $y=x , y=0$ and $x=8 $
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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If y satisfies the equation $\dfrac {dy}{dx}=x^2+y-1$ and with $y=1$ when $x=0$ using taylor series method for y about $x-0 $, find y when $x=0.1$ & $x=0.2$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Apply Runge kutta method of 4th order to find an approximate value of y at $x=0.2$ if $dy/dx=x+y^2$ given $y=1$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Apply Runge-kutta method of fourth order to find an approximate value of y at $x=1.2$ If $dy/dx=x^2+y^2$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Solve $\Bigg[y\Bigg(1+\dfrac 1x\Bigg)+\cos y\Bigg] dx+ (x+\log x-x\sin y)dy=0$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Evaluate the $\int\limits_0^1\int\limits_0^xe^{x+y}dydx$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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A square grassy plot is of side 100 metre.It has a gravel path 10 metres wide all round it on the inside. Find the area of path.
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Using the relation that length of the arc between two points A(x$_1$ , y$_1$) & B(x$_2$ , y$_2$) is given By $ s = \int_{x_1}^{x_2} \sqrt{(1+y')^2} \, dx $
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
2
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Evaluate $\int_{4}^{5.2}log_ex\,dx$ by using (i)Trapezoidal rule (ii) Simpson's 1/3 rule (iii) Simpson's 3/8 rule .
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Prove that $E=1+\triangle $
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Prove that $E = 1 + \triangle = e^{hD}$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Find by double integration, the area bounded by the lines $y=2+x,\,y=2-x,\,x=5$ .
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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The density at any point of a cardioide $r=a (1 + cos\theta)$ varies as the square of its distance from its axis of symmetry. Find its mass.
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Evaluate $\int_{0}^{2}\int_{0}^{x}\int_{0}^{2x+2y}e^{x+y+z}dz\,dy\,dx$ .
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Find the volume out off from the paraboloid $x^2+\frac{y^2}{4}+z=1$ by the plane z = 0.
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Evaluate $\iiint (x+y+z) \,dx\,dy\,dz$ over the tetrahedron bounded by the planes $x=0,y=0,z=0$ and $x+y+z=1$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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30k
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Evaluate $\iiint xyz \,dx\,dy\,dz$, over the positive octant of the sphere $x^2+y^2+z^2=a^2$ .
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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86) A cylindrical hole of radius $b$ is bored through a sphere of radius $a$. Find the volume of the remaining solid.
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Find the volume bounded by the cylinder $x^2+y^2=4$ and the planes $y+z=a$ and $z=0\cdot(H)$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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Find the volume in the first octant bounded by the cylinder $x^2 + y^2 = 2$ and the planes $z = x + y,\, y = x,\, z = 0$ and $x = 0(H)$
engineering mathematics updated 3.9 years ago by teamques10 ★ 70k
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